graph theoretic methods for matrix completion problems abstract a pattern is a list of positions in an n n real matrix a matrix completion problem for the class of matrices asks whether every partial matrix whose specified entries are exactly the positions of the pattern can be completed to a matrix we survey the current state of research on matrix completion problems for many subclasses of p 0 matrices including positive definite matrices m matrices inverse m matrices p matrices and matrices defined by various sign symmetry and positivity conditions on p 0 and p matrices graph theoretic techniques used to study completion problems are discussed several new results are also presented including the solution to the m 0 matrix completion problem and the sign symmetric p 0 matrix completion problem

fredholm transform and local rapid stabilization for a kuramoto sivashinsky equation this paper is devoted to the study of the local rapid exponential stabilization problem for a controlled kuramoto sivashinsky equation on a bounded interval we build a feedback control law to force the solution of the closed loop system to decay exponentially to zero with arbitrarily prescribed decay rates provided that the initial datum is small enough our approach uses a method we introduced for the rapid stabilization of a korteweg de vries equation it relies on the construction of a suitable integral transform and can be applied to many other equations

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

feedback control of the kuramoto sivashinsky equation abstract this work focuses on linear finite dimensional output feedback control of the kuramoto sivashinsky equation kse with periodic boundary conditions under the assumption that the linearization of the kse around the zero solution is controllable and observable linear finite dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution for any value of the instability parameter the controllers are synthesized on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the performance of the controllers is successfully tested through computer simulations

brief analysis and control of parabolic pde systems with input constraints this paper develops a general framework for the analysis and control of parabolic partial differential equations pde systems with input constraints initially galerkin s method is used for the derivation of ordinary differential equation ode system that capture the dominant dynamics of the pde system this ode systems are then used as the basis for the synthesis via lyapunov techniques of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed loop stability in the presence of constraints precise conditions that guarantee stability of the constrained closed loop parabolic pde system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator the theoretical results are used to stabilize an unstable steady state of a diffusion reaction process using constrained control action

stability of distributed parameter systems with finite dimensional controller compensators using singular perturbations abstract using a singular perturbation formulation of the linear time invariant distributed parameter system we develop a method to design finite dimensional feedback compensators of any fixed order which will stabilize the infinite dimensional distributed parameter system the synthesis conditions are given entirely in terms of a finite dimensional reduced order model the stability results depend on an infinite dimensional version of the klimushchev krasovskii lemma presented here

global carleman estimates for the linear stochastic kuramoto sivashinsky equations and their applications abstract in this paper we establish two new global carleman estimates for the linear stochastic kuramoto sivashinsky equations the first one is for the backward linear stochastic kuramoto sivashinsky equation based on this estimate and the duality argument we obtain the null controllability of the forward linear stochastic kuramoto sivashinsky equation by three controls one is an internal control in the diffusion term and the others are boundary controls the second one is for the forward linear stochastic kuramoto sivashinsky equation according to this estimate we obtain a unique continuation property for the forward linear stochastic kuramoto sivashinsky equation

model reduction of parabolic pdes using multivariate splines abstracta new methodology is presented for model reduction of linear parabolic partial differential equations pdes on general geometries using multivariate splines on triangulations state space descriptions are derived that can be used for control design this method uses galerkin projection with b splines to derive a finite set of ordinary differential equations odes any desired smoothness conditions between elements as well as the boundary conditions are flexibly imposed as a system of side constraints on the set of odes projection of the set of odes on the null space of the system of side constraints naturally produces a reduced order model that satisfies these constraints this method can be applied for both in domain control and boundary control of parabolic pdes with spatially varying coefficients on general geometries the reduction method is applied to design and implement feedback controllers for stabilisation of a 1 d unstable heat equation and a more challenging 2 d reaction convection d

dynamics and control of the 2 d navier stokes equations abstract this paper deals with the dynamics and control of the two dimensional 2 d navier stokes n s equations with a spatially periodic and temporally steady forcing term first we construct a dynamical system of nine nonlinear differential equations by fourier expansion and truncation of the 2 d n s equations then we study the dynamics of the obtained reduced order system by analyzing the system s attractors for different values of the reynolds number r e by applying the symmetry of the equations on one of the system s attractors a symmetric limit trajectory that is part of the dynamics is obtained moreover a lyapunov based control strategy to control the dynamics of the system for a given r e is designed finally numerical simulations are undertaken to validate the theoretical developments

the symmetric m matrix and symmetric inverse m matrix completion problems abstract the symmetric m matrix and symmetric m 0 matrix completion problems are solved and results of johnson and smith linear algebra appl 290 1999 193 are extended to solve the symmetric inverse m matrix completion problem 1 a pattern i e a list of positions in an n n matrix has symmetric m completion i e every partial symmetric m matrix specifying the pattern can be completed to a symmetric m matrix if and only if the principal subpattern r determined by its diagonal is permutation similar to a pattern that is block diagonal with each diagonal block complete or in graph theoretic terms if and only if each component of the graph of r is a clique 2 a pattern has symmetric m 0 completion if and only if the pattern is permutation similar to a pattern that is block diagonal with each diagonal block either complete or omitting all diagonal positions or in graph theoretic terms if and only if every principal subpattern corresponding to a component of the graph of the pattern either omits all diagonal positions or includes all positions 3 a pattern has symmetric inverse m completion if and only if its graph is block clique and no diagonal position is omitted that corresponds to a vertex in a graph block of order 2 the techniques used are also applied to matrix completion problems for other classes of symmetric matrices

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

stability enhancing control of a coupled transport diffusion system with dirichlet actuation and dirichlet measurement abstract we investigate the problem of enhancing the stability of a coupled transport diffusion system with dirichlet actuation and dirichlet measurement in the recent paper h sano neumann boundary control of a coupled transport diffusion system with boundary observation j math anal appl 377 2011 807 816 we treated the stabilization problem for the case with neumann actuation and dirichlet measurement where the variable transformation of the state is performed by using the fractional power of an unbounded operator however we cannot use the similar transformation for the case with dirichlet actuation and dirichlet measurement since it brings an ill posed expression of the system so we use an algebraic approach for the formulation of the system in this paper it is shown that a reduced order model with a finite dimensional state variable is controllable and observable the fact enables us to construct a finite dimensional stability enhancing controller for the original infinite dimensional system by using a residual mode filter rmf approach the novelty of this paper is the structure that the controller contains the dynamics with respect to the control variable as a result the state vector of the resulting closed loop system includes the control variable as its entry

compensator design of semi linear parabolic systems the stabilization of semi linear parabolic distributed systems by means of boundary controls is treated formulating the partial differential equation describing the system as an evolution equation in a hilbert space here by using the properties of an analytic semigroup the global existence of the solution under static output feedback is shown moreover in the similar way the global existence of the solution and the stabihzability for the system which installs a finite dimensional dynamic compensator is shown

global stabilization of the kuramoto sivashinsky equation via distributed output feedback control abstract this work addresses the problem of global exponential stabilization of the kuramoto sivashinsky equation kse subject to periodic boundary conditions via distributed static output feedback control under the assumption that the number of measurements is equal to the total number of unstable and critically stable eigenvalues of the kse and a necessary and sufficient stability condition is satisfied linear static output feedback controllers are designed that globally exponentially stabilize the zero solution of the kse the controllers are designed on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the theoretical results are confirmed by computer simulations of the closed loop system

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

completions of inverse m matrix patterns abstract a list of positions in an n n real matrix that includes all diagonal positions a pattern is said to have inverse m completion if every partial inverse m matrix that specifies exactly these positions can be completed to an inverse m matrix johnson and smith c r johnson r l smith linear algebra and its applications 241 243 1996 655 667 characterize the positionally symmetric patterns that have inverse m completion as those patterns whose graphs are block clique in this paper the restriction of positional symmetry is removed a pattern has inverse m completion if and only if the digraph g of the pattern has the properties a the induced subdigraph of a cycle is a clique and b if g contains both arc i j and a path of length 1 between i and j then the induced subdigraph of the path is a clique furthermore any irreducible pattern with inverse m completion is positionally symmetric and has a block clique digraph any pattern is permutation similar to a block lower triangular pattern with irreducible diagonal blocks and such a pattern has inverse m completion if and only if i the pattern digraph of each diagonal block is block clique ii each subdiagonal block contains at most one position and iii the pattern digraph of the block structure has no alternate path to a single arc

the completion problem for m matrices and inverse m matrices abstract the completion problems for m matrices and inverse m matrices are discussed the former has a simple solution but is not at all analogous to the positive definite completion problem the latter is more subtle and is analogous to the positive definite problem a graph theoretic completion result as well as a determinant maximizing completion that is characterized by having a zero entry in the inverse in every position in which the partial matrix has an unspecified entry is given for the inverse m matrix problem these mirror to some extent the positive definite case but the methodology is necessarily different

local exact controllability to the trajectories of the 1 d kuramoto sivashinsky equation abstract we are concerned with the boundary controllability to the trajectories of the kuramoto sivashinsky equation by using a carleman estimate we obtain the null controllability of the linearized equation around a given solution from a local inversion theorem we get the local controllability to the trajectories of the nonlinear system

spillover stabilization in finite dimensional control and observer design for dissipative evolution equations we consider the problem of global stabilization of a semilinear dissipative evolution equation by finite dimensional control with finite dimensional outputs coupling between the system modes occurs directly through the nonlinearity and also through the control influence functions similar modal coupling occurs in the infinite dimensional error dynamics through the nonlinearity and measurements for both the control and observer designs rather than decompose the original system into fourier modes we consider lyapunov functions based on the infinite dimensional dynamics of the state and error systems respectively the inner product terms of the lyapunov derivative are decomposed into fourier modes upper bounds on the terms representing control and observation spillover are obtained linear quadratic regulator lqr designs are used to stabilize the state and error systems with these upper bounds relations between system and lqr design parameters are given to ensure global stability of the state and error dynamics with robustness with respect to control and observation spillover respectively it is shown that the control and observer designs can be combined to yield a globally stabilizing compensator the control and observer designs are numerically demonstrated on the problem of controlling stall in a model of axial compressors

a galerkin neural network based design of guaranteed cost control for nonlinear distributed parameter systems this paper presents a galerkin neural network based guaranteed cost control gcc design for a class of parabolic partial differential equation pde systems with unknown nonlinearities a parabolic pde system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement motivated by this in the proposed control scheme galerkin method is initially applied to the pde system to derive an ordinary differential equation ode system with unknown nonlinearities which accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently parameterized by a multilayer neural network mnn with one hidden layer and zero bias terms then based on the neural model and a lure type lyapunov function a linear modal feedback controller is developed to stabilize the closed loop pde system and provide an upper bound for the quadratic cost function associated with the finite dimensional slow system for all admissible approximation errors of the network the outcome of the gcc problem is formulated as a linear matrix inequality lmi problem moreover by using the existing lmi optimization technique a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained finally the proposed design method is applied to the control of the temperature profile of a catalytic rod

inverse m matrix completions of patterns omitting some diagonal positions abstract let n 1 n which subsets q of n n have the property that whenever a ij for i j q form a partial inverse m matrix i e a ij 0 and if l l q then the inverse of a ij i j l is an m matrix a ij can be defined for i j q so that the inverse of a a ij is an m matrix in terms of a digraph g with vertex set n and arcs i j q with i j our results say 1 it is necessary that the induced subdigraph of any alternate path to an arc be a clique 2 a cycle need not be contained in a clique if i i q for at least one vertex i of 3 when n 4 it is necessary and sufficient that condition 1 is true and every simple cycle has a vertex i with i i q and 4 the general question can be reduced to the case in which g is strongly connected much as it has been when q contains i i for every i n

drag reduction in transitional linearized channelow using distributed control this work focuses on feedback control of incompressible transitional newtonian channel flow described by the twodimensional linearized navier stokes equations the control objective is to use distributed feedback to achieve stabilization of the parabolic velocity profile for values of the reynolds number for which this profile is unstable and therefore to reduce the frictional drag exerted on the lower channel wall compared to the open loop values the control system uses measurements of shear stresses on the lower channel wall and the control actuation is assumed to be in the form of electromagnetic lorentz forces applied to the flow near the bottom wall galerkin s method is initially used to derive a high order discretization of the linearized flow field that captures the flow instability and accounts for the effect of control actuation on all the modes then a low order approximation of the linearized flow field is derived and used for the synthesis of a linear output feedback controller that enfor

modified gronwall s inequality and its application to stabilization problem for semilinear parabolic systems abstract this paper deals with the stabilization of semilinear parabolic distributed systems by means of boundary controls the partial differential equation describing the system is formulated as a semilinear evolution equation in a hilbert space by using a variable transformation here it is shown that the solution globally exists for the closed loop system which installs a finite dimensional dynamic compensator by using the properties of an analytic semigroup moreover a sufficient condition for stabilization of the system is derived by making use of the modified gronwall s inequality developed in this paper

brief robust control of parabolic pde systems with time dependent spatial domains we synthesize robust nonlinear static output feedback controllers for systems of quasi linear parabolic partial differential equations with time dependent spatial domains and uncertain variables the controllers are successfully applied to a typical diffusion reaction process with moving boundary and uncertainty

an application of inertial manifold theory to boundary stabilization of semilinear diffusion systems this paper deals with an application of inertial manifold theory to boundary stabilization of semilinear diffusion systems on a one dimensional domain it is shown that a sakawa type of controller plays an important role in the construction of an inertial manifold for the closed loop system with a given semilinear diffusion system this means that the use of a sakawa type of controller reduces the stabilization problem for the closed loop system to the one on the inertial manifold

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

a sampled data singularly perturbed boundary control for a heat conduction system with noncollocated observation this note presents a sampled data strategy for a boundary control problem of a heat conduction system modeled by a parabolic partial differential equation pde using the zero order hold the control law becomes a piecewise constant signal in which a step change of value occurs at each sampling instant through the dasialiftingpsila technique the pde is converted into a sequence of constant input problems to be solved individually for a sampled data formulation the eigenspectrum of the parabolic system can be partitioned into two groups a finite number of slow modes and an infinite number of fast modes which is studied via the theory of singular perturbations controllability and observability of the sampled data system are preserved irrelevant to the sampling period a noncollocated output feedback design based upon the state observer is employed for set point regulation the state observer serves as an output feedback compensator with no static feedback directly from the output satisfying the so called dasialow pass propertypsila the feedback controller is thus robust against the observation error due to the neglected fast modes

finite dimensional compensator design for parabolic distributed systems with point sensors and boundary input a compensator design is proposed for a large class of parabolic distributed systems basically it is a modal approach utilizing known finite dimensional algorithms for observer and stabilizer design the observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a distributed or boundary implementation explicit sufficient conditions are given for the convergence of this scheme

feedback stabilization of linear diffusion systems this paper treats the feedback stabilization of linear diffusion systems by using a finite dimensional feedback dynamic controller we construct a finite dimensional observer using the output functions from sensors and the control inputs to the system are given by the feedback of the observer output assuming for some fixed finite number l that the first l modes are controllable and observable we prove that it is possible to construct a finite dimensional feedback dynamic controller such that the diffusion system has an arbitrarily large damping constant

distributed fuzzy control design of nonlinear hyperbolic pde systems with application to nonisothermal plug flow reactor this paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first order hyperbolic partial differential equations pdes where the control actuators are continuously distributed in space the goal of this paper is to develop a fuzzy state feedback control design methodology for these systems by employing a combination of pde theory and concepts from takagi sugeno t s fuzzy control first the t s fuzzy hyperbolic pde model is proposed to accurately represent the nonlinear first order hyperbolic pde system subsequently based on the t s fuzzy pde model a lyapunov technique is used to analyze the closed loop exponential stability with a given decay rate then a fuzzy state feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities sdlmis from the resulting stability conditions furthermore utilizing the finite difference approximation method with a backward difference for the spatial derivative a recursive algorithm is presented to solve the sdlmis via the existing lmi optimization techniques finally the developed design methodology is successfully applied to the control of a nonisothermal plug flow reactor

using lyapunov s direct method for wave suppression in reactive systems this paper proposes a new approach for stabilizing a homogeneous solution in reaction convection diffusion system with oscillatory kinetics in which moving or stationary patterns emerge in the absence of control specifically we aim to suppress patterns by using a spatially weighted finite dimensional feedback control that assures stability of the solution according to lyapunov s direct method a practical design procedure based on spectral representation of the system and the dissipative nature of parabolic pdes is presented 2006 elsevier b v all rights reserved

nonlinear control of incompressible fluid flow application to burgers equation and 2d channel flow abstract this paper proposes a methodology for the synthesis of nonlinear finite dimensional feedback controllers for incompressible newtonian fluid flows described by two dimensional navier stokes equations combination of galerkin s method with approximate inertial manifolds is employed for the derivation of low order ordinary differential equation ode systems that accurately describe the dominant dynamics of the flow these ode systems are subsequently used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed loop system to follow the reference input asymptotically the method is successfully used to synthesize nonlinear finite dimensional output feedback controllers for the burgers equation and the two dimensional channel flow that enhance the convergence rate to the spatially uniform steady state and the parabolic velocity profile respectively the performance of the proposed controllers is successfully tested through simulations and is shown to be superior to the one of linear controllers

finite dimensional compensators for infinite dimensional systems with unbounded input operators this paper contains a design procedure for constructing finite dimensional compensators for a class of infinite dimensional systems with unbounded input operators applications to retarded functional differential systems with delays in the input or the output variable and to partial differential equations with boundary input operators are discussed

stabilization of a coupled transport diffusion system with boundary input we consider the problem of stabilizing a coupled transport diffusion system with boundary input the system is described by two linear transport diffusion equations and is not asymptotically stable in order to stabilize the system with boundary input sensor influence functions are assumed to be located at interior of the domain first we formulate the system as an evolution equation with unbounded output operators in a hilbert space using variable transformation next we derive a reduced order model with a finite dimensional state variable for the infinite dimensional system then a stabilizing controller is constructed for the reduced order model under an additional assumption it is shown that the finite dimensional controller together with a residual mode filter plays a role of a finite dimensional stabilizing controller for the original infinite dimensional system if the order of the residual mode filter is chosen sufficiently large finally the validity of the design method is demonstrated through a numerical simulation

neumann boundary control of a coupled transport diffusion system with boundary observation abstract we study the neumann boundary stabilization problem of a coupled transport diffusion system in the case where the observation is done at the boundary in the recent paper of sano and nakagiri h sano s nakagiri stabilization of a coupled transport diffusion system with boundary input j math anal appl 363 2010 57 72 we treated the stabilization problem for the case with neumann boundary control and distributed observation the novelty of this paper is the formulation of the boundary observation equation in a hilbert space we have an interesting result of its being expressed by using an a 1 bounded operator with 1 2 1 moreover it is shown that a reduced order model with a finite dimensional state variable is controllable and observable this means that one can always construct a finite dimensional stabilizing controller for the original infinite dimensional system by using a residual mode filter rmf approach

nonlinear finite dimensional control of a class of nonlinear distributed parameter systems using residual mode filters a proof of local exponential stability abstract in any attempt to control an infinite dimensional distributed parameter system dps with a finite dimensional controller some compensation for deleterious controller interaction with unmodeled modes is needed we introduce the concepts of both a finite dimensional nonlinear controller based on any reasonable nonlinear reduced order model of the dps and stability compensation by a finite dimensional nonlinear residual mode filter under appropriate lipschitz continuity conditions on the nonlinearities this new pair of interconnected finite dimensional systems will produce closed loop exponentially stable control of the nonlinear dps

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

robust feed back control of travelling waves in a class of reaction diffusion distributed biological systems abstract reaction diffusion rd mechanisms can describe many biological phenomena such as neuron firing in the brain the heartbeat cellular organization activities or even biological disorders such as fibrillation the fitzhugh nagumo fhn model is a particular case of rd systems it is able to capture the key features of many biological processes and since it is relatively simple it has been widely employed during recent years some examples of its predictive capabilities include the representation of the normal behavior of some physiological phenomena related to a travelling plane wave as well as biological disorders associated with spiral or irregular fronts the objective of this work is to design a control law that is able to stabilize complex behaviors travelling plane wave in biological systems using the fhn model as a case study since in biological systems there usually exists a lack of detailed information on the system structure our control law will be designed to be robust i e it must be able to reach the predefined reference regardless the presence of structural uncertainties to this purpose we will extend some classical results on the finite dimensional robust control theory to rd systems by means of order reduction techniques in particular the proper orthogonal decomposition method

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

robust stabilization of the distributed parameter system with time delay via fuzzy control in this paper stabilization of the distributed parameter system dps with time delay is studied using galerkin s method and fuzzy control with the help of galerkin s method the dynamics of dps with time delay can be first converted into a group of low order functional ordinary differential equations which will be used for design of the robust fuzzy controller the fuzzy controller designed can guarantee exponential stability of the closed loop dps some sufficient conditions are derived for the stabilization together with the linear matrix inequality design approach the effectiveness of the proposed control design methodology is demonstrated in numerical simulations

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

finite dimensional h control of a class of infinite dimensional linear time varying systems in this paper we consider h control of infinite dimensional linear time varying idltv systems whose homogeneous parts are of modal type by using a finite dimensional controller the aim is to construct a finite dimensional stabilizing controller for the idltv system that makes the norm of the closed loop operator less than a given positive number to this end a finite dimensional model is firstly derived for the idltv system and a stabilizing controller that makes the norm of the closed loop operator less than another positive number is constructed for the finite dimensional model then it is shown that a controller which consists of a residual mode filter and the controller mentioned above becomes a finite dimensional stabilizing controller for the given idltv system such that the closed loop operator has norm less than if the order of the residual mode filter is chosen sufficiently large

the steady states of the kuramoto sivashinsky equation abstract the kuramoto sivashinsky equation is one of the simple nonlinear partial differential equations it represents a system in which the transport of energy through nonlinear mode coupling produces a balance between long wavelength instability and short wavelength dissipation the steady states and their stabilities give a foundation for understanding the dynamics of the system they are distinguished according to their energy levels and fall into different branches that are identified by their harmonic content various types of solution include laminar states n cell states long wave distorbed n cell states the giant states and steady traveling solutions the linear stability around the steady states gives a guide to the origin of additional steady states through bifurcation and to the identification of each steady state the index rule is also useful conjectured form the numerical observation the parameter dependence of the steady traveling waves is estimated in the limit of large values of the parameter in addition a singular perturbation calculation of traveling waves near bifurcation is carried out the dynamics of a system can be guided by the systematic study of the bifurcation and stability for example if all the stationary and periodic solutions are unstable for some parameter range chaotic behavior of the system is expected since any orbit governed by the equation has to wander around forever in the phase space the orbits will then lie on strange attractors

a new global carleman estimate for the one dimensional kuramoto sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem abstract in this paper we establish a new global carleman estimate for the linearized kuramoto sivashinsky equation which is a one parameter carleman estimate based on this estimate we can obtain the local exact controllability to the trajectories and lipschitz stability in an inverse problem for the kuramoto sivashinsky equation

nonlinear feedback control of parabolic partial differential equation systems with time dependent spatial domains partial differential equations pdes with time dependent spatial domains whose dynamics can be partitioned into slow and fast ones initially a nonlinear model reduction scheme similar to the one introduced in christofides and daoutidis j math anal appl 216 1997 398 420 which is based on combinations of galerkin s method with the concept of approximate inertial manifold is employed for the derivation of low order ordinary differential equation ode systems that yield solutions which are close up to a desired accuracy to the ones of the pde system for almost all times then these ode systems are used as the basis for the explicit construction of nonlinear time varying output feedback controllers via geometric control methods the controllers guarantee stability and enforce the output of the closed loop parabolic pde system to follow up to a desired accuracy a prespecified response for almost all times provided that the separation of the slow and fast dynamics is sufficiently large differences in the nature of the model reduction and control problems between parabolic pde systems with fixed and moving spatial domains are identified and discussed the proposed control method is used to stabilize an unstable steady state of a diffusion reaction process whose spatial domain changes with time it is shown to lead to a significant reduction on the order of the stabilizing nonlinear output feedback controller and outperform a nonlinear controller synthesis method that does not account for the variation of the spatial domain q 1999 academic press

on approximate inertial manifolds to the navier stokes equations abstract recently the theory of inertial manifolds has shown that the long time behavior the dynamics of certain dissipative partial differential equations can be fully discribed by that of a finite ordinary differential system although we are still unable to prove existence of inertial manifolds to the navier stokes equations we present here a nonlinear finite dimensional analytic manifold that approximates closely the global attractor in the two dimensional case and certain bounded invariant sets in the three dimensional case this approximate manifold and others allow us to introduce modified galerkin approximations

back in the saddle again a computer assisted study of the kuramoto sivashinsky equation a numerical and analytical study of the kuramoto sivashinsky partial differential equation pde in one spatial dimension with periodic boundary conditions is presented the structure stability and bifurcation characteristics of steady state and time dependent solutions of the pde for values of the parameter alpha less than 40 are examined the numerically observed primary and secondary bifurcations of steady states as well as bifurcations to constant speed traveling waves limit cycles are analytically verified persistent homoclinic and heteroclinic saddle connections are observed and explained via the system symmetries and fixed point subspaces of appropriate isotropy subgroups of o 2 their effect on the system dynamics is discussed and several tertiary bifurcations observed numerically are presented

finite dimensional control of parabolic pde systems using approximate inertial manifolds abstract this paper introduces a methodology for the synthesis of nonlinear finite dimensional output feedback controllers for systems of quasi linear parabolic partial differential equations pdes for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement combination of galerkin s method with a novel procedure for the construction of approximate inertial manifolds for the pde system is employed for the derivation of ordinary differential equation ode systems whose dimension is equal to the number of slow modes that yield solutions which are close up to a desired accuracy to the ones of the pde system for almost all times these ode systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed loop system to follow up to a desired accuracy a prespecified response for almost all times

unsteady two dimensional flows in complex geometries comparative bifurcation studies with global eigenfunction expansions we present a bifurcation study of the incompressible navier stokes equations in a model complex geometry a spatially periodic array of cylinders in a channel the dynamics of the flow include a hopf bifurcation from steady to oscillatory flow at an approximate reynolds number r of 350 and the appearance of a second frequency at approximately r simeq 890 the multiple frequency dynamics include a substantial increase in spatial and temporal scales with reynolds number as compared with the simple limit cycle oscillation present close to r 350 numerical bifurcation studies of the dynamics are performed using three forms of global eigenfunction expansions the first basis set is derived through principal factor analysis karhunen loeve expansion of snapshots from accurate direct spectral element numerical solutions of the navier stokes equations the second set is obtained from the eigenfunctions of the stokes operator for this geometry finally eigenfunctions are derived from a singular stokes operator i e the stokes operator modified to include a variable coefficient which vanishes at the domain boundaries truncated systems of sim 100 odes are obtained through projection of the navier stokes equations onto the basis sets and a comparative study of the resulting dynamical models is performed

embedded localization band in undrained soil based on regularized strong discontinuity theory and fe analysis abstract the paper presents a novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid filled pores where the solid phase is considered as elastic plastic the basic feature is the concept of regularized displacement and pore pressure discontinuities which are assumed to occur across an internal discontinuity surface in this respect the present developments are extensions of those suggested by simo et al 1993 comput mech 12 277 296 and more recently by larsson and runesson 1995 j engng mech asce in press a finite element formulation is proposed on the basis of a mixed variational formulation in the spirit of the enhanced strain concept by simo and rifai 1990 int j numer meth engng 29 1595 1638 in this fashion the localization zone is embedded into a base element for the ordinary analysis of the non localized mixture problem

completions of partial p matrices with acyclic or non acyclic associated graph abstract in this paper we analyze the positive sign symmetric p matrix completion problem when the pattern of the partial matrix is non symmetric we prove that every positive sign symmetric partial p matrix a has a positive sign symmetric p matrix completion when the associated graph of the specified entries of a g a is acyclic and we study special cases when g a is not acyclic

process systems and passivity via the clausius planck inequality in this paper we define a process system to be a system which has actions with the clausius planck and conservation properties we use standard and well established results derived from macroscopic thermodynamics to show that a process system has actions which satisfy the dissipation inequality furthermore these actions have an inner product structure and a link between the thermodynamic theory of process systems and the input output passivity theory of nonlinear control is established the paper therefore represents a step towards developing a passivity based approach for distributed control system design for chemical processes a review of relevant concepts from thermodynamics is given in an appendix

on completion problems for various classes of p matrices abstract a p matrix is a real square matrix having every principal minor positive and a fischer matrix is a p matrix that satisfies fischer s inequality for all principal submatrices in this paper all patterns of positions for n n matrices n 4 are classified as to whether or not every partial matrix can be completed to a matrix for any of the classes positive p nonnegative p or fischer matrices also all symmetric patterns for 5 5 matrices are classified as to completion of partial fischer matrices and all but two such patterns are classified as to positive p or nonnegative p completion we also show that any pattern whose digraph contains a minimally chordal symmetric hamiltonian induced subdigraph does not have completion for any of the classes positive p nonnegative p fischer matrices

optimal control of a distributed hyperbolic system with multiple time varying lags in this paper an optimal distributed control problem for a hyperbolic system in which different multiple time varying lags appear both in the state equation and in the boundary condition is considered making use of lion s scheme necessary and sufficient conditions of optimality for the neumann problem with the quadratic performance functional and constrained control are derived a simple example of application is also presented

stability enhancement by boundary control in the kuramoto sivashinsky equation where we refer to 0 as the anti di ussion parameter note that a more general form ut 1uxxxx 2uxx 3uux 0 can always be reduced to 1 1 by appropriate rescaling of t x and u eq 1 1 was derived independently by kuramoto et al 20 22 as a model for phase turbulence in reaction di usion systems and by sivashinsky 33 as a model for plane ame propagation describing the combined in uence of di usion and thermal conduction of the gas on stability of a plane ame front so far it has been well understood that the ks equation can also serve as a mathematical model for cellular instabilities in a variety of situations the ow of thin liquid lms on inclined planes 30 in the limit of large surface tension dendritic fronts in dilute binary alloys 31 and alfven drift waves in plasmas 23 as a nonlinear saturation mechanism of the dissipative trapped ion modes

finite dimensional approximation and control of non linear parabolic pde systems this article proposes a rigorous and practical methodology for the derivation of accurate finite dimensional approximations and the synthesis of non linear output feedback controllers for non linear parabolic pde systems for which the manipulated inputs the controlled and measured outputs are distributed in space the method consists of three steps first the karhunen loeve expansion is used to derive empirical eigenfunctions of the non linear parabolic pde system then the empirical eigenfunctions are used as basis functions within a galerkin s and approximate inertial manifold model reduction framework to derive low order ode systems that accurately describe the dominant dynamics of the pde system and finally these ode systems are used for the synthesis of non linear output feedback controllers that guarantee stability and enforce output tracking in the closed loop system the proposed method is used to perform model reduction and synthesize a non linear dynamic output feedback controller for a rapi

robust output feedback control of quasi linear parabolic pde systems abstract this paper proposes a methodology for the synthesis of nonlinear robust output feedback controllers for systems of quasi linear parabolic partial differential equations with time varying uncertain variables the method is successfully applied to a typical diffusion reaction process with uncertainty

finite dimensional controllers for linear distributed parameter systems exponential stability using residual mode filters abstract modal control has often been proposed as a way to design stabilizing low order controllers for distributed parameter systems dps however it is well known that such controllers designed from a reduced order modal model do not necessarily stabilize the actual dps in this paper we prove that exponential closed loop stability can always be achieved by the addition of a residual mode filter of sufficiently large dimension

redheffer s lemma and h_ infty control for infinite dimensional systems an infinite dimensional version of a lemma that has been crucial in the theory of h infty control with measurement feedback for finite dimensional systems is proved this extension is used to parametrize all controllers that solve the suboptimal h infty control problem for a large class of infinite dimensional systems

robust adaptive boundary control of a flexible marine riser with vessel dynamics in this paper robust adaptive boundary control for a flexible marine riser with vessel dynamics is developed to suppress the riser s vibration to provide an accurate and concise representation of the riser s dynamic behavior the flexible marine riser with vessel dynamics is described by a distributed parameter system with a partial differential equation pde and four ordinary differential equations odes boundary control is proposed at the top boundary of the riser based on lyapunov s direct method to regulate the riser s vibration adaptive control is designed when the system parametric uncertainty exists with the proposed robust adaptive boundary control uniform boundedness under the ocean current disturbance can be achieved the proposed control is implementable with actual instrumentation since all the required signals in the control can be measured by sensors or calculated by a backward difference algorithm the state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters simulations are provided to illustrate the applicability and effectiveness of the proposed control

quasi equilibrium grid algorithm geometric construction for model reduction the method of invariant grid mig is an iterative procedure for model reduction in chemical kinetics which is based on the notion of slow invariant manifold sim a n gorban i v karlin method of invariant manifold for chemical kinetics chem eng sci 58 2003 4751 4768 e chiavazzo a n gorban i v karlin comparison of invariant manifolds for model reduction in chemical kinetics commun comput phys 2 5 2007 964 992 a n gorban i v karlin a y zinovyev invariant grids for reaction kinetics physica a 333 2004 106 154 a n gorban i v karlin invariant manifolds for physical and chemical kinetics lecture notes physics 660 springer berlin heidelberg 2005 doi 10 1007 b98103 important role in that method is played by the initial grid which once refined gives a description of the invariant manifold the invariant grid a convenient way to get a first approximation of the sim is given by the spectral quasi equilibrium manifold sqem a n gorban i v karlin method of invariant manifold for chemical kinetics chem eng sci 58 2003 4751 4768 e chiavazzo a n gorban i v karlin comparison of invariant manifolds for model reduction in chemical kinetics commun comput phys 2 5 2007 964 992 in the present paper a flexible numerical method to construct the discrete analog of a quasi equilibrium manifold in any dimension is presented that object is named quasi equilibrium grid qeg while the procedure quasi equilibrium grid algorithm qega extensions of the qem notion are also suggested the qega is a numerical tool which can be used to find a grid based approximation for the locus of minima of a convex function under some linear constraints the method is validated by construction of one and two dimensional grids for a model of hydrogen oxidation reaction

dynamical analysis of distributed parameter tubular reactors this paper is dedicated to the dynamical analysis of tubular reactor models namely plug flow and axial dispersion reactors involving sequential reactions for which the kinetics only depends on the concentrations of the reactants involved in the reaction this analysis is performed by describing these models as infinite dimensional state space systems with bounded observation and control operators it is shown that these systems are exponentially stable and that a the plug flow reactor model is observable when the component concentrations are measured at the reactor output and observable with respect to its physical domain when only the product concentration is measured and it is reachable with respect to its physical domain when it is controlled at the reactor input and b any finite set of dominant modes of the axial dispersion reactor model is observable when either all the component concentrations or only the product concentration are measured and reachable by using appropriate sensors and actuators the dynamical properties of related finite dimensional models are also discussed

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

lq optimal boundary control of infinite dimensional systems with yosida type approximate boundary observation a class of boundary control systems with boundary observation is considered for which the unbounded operators often lead to technical difficulties an extended model for this class of systems is described and analyzed which involves no unbounded operator except for the dynamics generator a method for the resolution of the lq optimal control problem for this model is described and the solution provides a stabilizing feedback for the nominal system with unbounded operators in the sense that in closed loop the state trajectories converge to zero exponentially fast the model consists of an extended abstract differential equation whose state components are the boundary input the state up to an affine transformation and a yosida type approximation of the output of the nominal system it is shown that under suitable conditions the model is well posed and in particular that the dynamics operator is the generator of a c 0 semigroup moreover the model is shown to be observable and to carry controllability stabilizability and detectability properties from the nominal system a general method of resolution based on the problem of spectral factorization of a multi dimensional operator valued spectral density is described in order to solve a lq optimal control problem for this model it is expected that this approach will lead hopefully to a good trade off between the cost of modeling and the efficiency of methods of resolution of control problems for such systems

non linear feedback control of parabolic partial differential difference equation systems this paper proposes a general method for the synthesis of non linear output feedback controllers for single input singleoutput quasi linear parabolic partial differential difference equation pdde systems for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement initially a non linear model reduction scheme which is based on combination of galerkin s method with the concept of approximate inertial manifold is employed for the derivation of differential difference equation dde systems that describe the dominant dynamics of the pdde system then these dde systems are used as the basis for the explicit construction of non linear output feedback controllers through combination of geometric and lyapunov techniques the controllers guarantee stability and enforce output tracking in the closed loop parabolic pdde system independently of the size of the state delay provided that the separation o

completions of p matrix patterns abstract a list of positions in an n n real matrix a pattern is said to have m completion if every partial m matrix that specifies exactly these positions can be completed to an m matrix let q be a pattern that includes all diagonal entries and let g be its digraph the following are equivalent 1 the pattern q has m completion 2 the pattern q is permutation similar to a block triangular pattern with all the diagonal blocks completely specified 3 any strongly connected subdigraph of g is complete a pattern with some diagonal entries unspecified has m completion if and only if the principal subpattern defined by the specified diagonal positions has m completion

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

matrix completion problems for pairs of related classes of matrices abstract for a class x of real matrices a list of positions in an n n matrix a pattern is said to have x completion if every partial x matrix that specifies exactly these positions can be completed to an x matrix if x and x0 are classes that satisfy the conditions any partial x matrix is a partial x0 matrix for any x0 matrix a and e 0 a ei is a x matrix and for any partial x matrix a there exists 0 such that a i is a partial x matrix where is the partial identity matrix specifying the same pattern as a then any pattern that has x0 completion must also have x completion however there are usually patterns that have x completion that fail to have x0 completion this result applies to many pairs of subclasses of p and p0 matrices defined by the same restriction on entries including the classes p p0 matrices weakly sign symmetric p p0 matrices and non negative p p0 matrices it also applies to other related pairs of subclasses of p0 matrices such as the pairs classes of p p0 1 matrices weakly sign symmetric p p0 1 matrices and non negative p p0 1 matrices furthermore any pattern that has weakly sign symmetric sign symmetric non negative p0 completion must also have weakly sign symmetric sign symmetric non negative p0 1 completion although these pairs of classes do not satisfy condition 3 similarly the class of inverse m matrices and its topological closure do not satisfy condition 3 but the conclusion remains true and the matrix completion problem for the topological closure of the class of inverse m matrices is solved for patterns containing the diagonal

neumann boundary stabilization of one dimensional linear parabolic systems with input delay this paper addresses the boundary stabilization problem of one dimensional linear parabolic systems with input delay especially the case of neumann boundary control is studied the purpose is to derive the stabilizing controller of predictor type in a hilbert space by using a backstepping method combined with the semigroup theory the use of the semigroup theory makes the proof of continuity of the inverse transformation easy also it is shown that the implementation of the abstract controller is feasible by using a finite number of eigenvalues and eigenfunctions of the system operator

predictive control with guaranteed stability for water hammer equations we study the application of the receding horizon optimal control rhoc for hydraulic pipeline systems described by the so called water hammer equations sufficient conditions to guarantee an asymptotic stability to an equilibrium state are first introduced and then integrated in the rhoc scheme for the implementation calculus of variations is employed to characterize the optimal solution in terms of the adjoint state and the recently proposed lattice boltzmann method is used to solve both direct and adjoint partial differential equations this approach is finally validated in simulation

distributed parameter thermal controllability a numerical method for solving the inverse heat conduction problem this paper addresses the inverse heat conduction problem encountered in thermal manufacturing processes a numerical control algorithm is developed for distributed parameter conduction systems based on galerkin optimization of an energy index employing green s functions various temperature profiles of variable complexity are studied using the proposed technique in order to determine the surface heat input distribution necessary to generate the desired temperature field inside a solid body furthermore the effect of altering the iterative time step and duration of processing time on the convergence of the solution generated by the aforementioned method is investigated it is proved that despite the variations in numerical processing the iterative technique is able to solve the problem of inverse heat conduction in the thermal processing of materials copyright 2004 john wiley sons ltd

on the stability of a linear bioprocess model with recycle loop in this note we treat a linear bioprocess model with recycle loop and analyze the spectrum of the closed loop operator in order to discuss the exponential stability it is shown that a c sub 0 semigroup generated by the closed loop operator satisfies the spectrum determined growth assumption and that the recycle loop works effectively for the process through a numerical simulation

a localization capturing fe interface based on regularized strong discontinuities at large inelastic strains the objective of this work is the development of a finite element interface formulation tailored to capture localization within geometrically nonlinear solid mechanics in this context strong discontinuities are considered as the final failure mechanism within localization problems the failure kinematics are governed by a jump in the nonlinear deformation map across a discontinuity surface in the finite element discretization the interface element is endowed with these kinematics as a consequence the interface stiffness is dominated by the weighted spatial localization tensor based on these developments a localization capturing procedure is advocated and is computationally highlighted

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given