a domain decomposition method based on weighted interior penalties for advection diffusion reaction problems we propose a domain decomposition method for advection diffusion reaction equations based on nitsche s transmission conditions the advection dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries we prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method the convergence of the resulting domain decomposition method is proved and this result holds true uniformly with respect to the diffusion parameter the numerical scheme that we propose here can thus be applied straightforwardly to diffusion dominated advection dominated and hyperbolic problems some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method and we compare our method with some other domain decomposition techniques for advection diffusion equations

control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

time varying input and state delay compensation for uncertain nonlinear systems a robust controller is developed for uncertain second order nonlinear systems subject to simultaneous unknown time varying state delays and known sufficiently small time varying input delays in addition to additive sufficiently smooth disturbances an integral term composed of previous control values facilitates a delay free open loop error system and the development of the feedback control structure a stability analysis based on lyapunov krasovskii lk functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays

two level overlapping schwarz algorithms for a staggered discontinuous galerkin method two overlapping schwarz algorithms are developed for a discontinuous galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions the discontinuous galerkin formulation is based on a staggered discretization introduced by chung and engquist siam j numer anal 47 2009 pp 3820 3848 for the acoustic wave equation two types of coarse problems are introduced for the two level schwarz algorithms the first is built on a nonoverlapping subdomain partition which allows quite general subdomain partitions and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation condition number bounds are established and numerical results are presented

robustness and safe sampling of distributed delay control laws for unstable delayed systems in the control of delayed systems by a finite spectrum assignment fsa in the control law the integral over the time delay of a function of past control appears this assignment is in fact available for continuous delayed process independently of the stability of the latter which is very interesting since smith predictor is usually only used with stable processes nevertheless in case of fsa control implementation this integral control should be sampled so that spectrum assignment is not necessarily preserved and an unstable discrete closed loop can be obtained in this technical note fsa integral control robustness with respect to prediction time uncertainty is analyzed for an unstable continuous linear system a transformation approach is also proposed to understand the effects of different ways of sampling control laws in a last part a case study shows how simpson approximation of integral control law leads to an unstable digital closed loop

a bddc algorithm for a class of staggered discontinuous galerkin methods a bddc balancing domain decomposition by constraints algorithm is developed and analyzed for a staggered discontinuous galerkin dg finite element approximation of second order scalar elliptic problems on a quite irregular subdomain partition an optimal condition number bound is proved for two dimensional problems in addition a sub optimal but scalable condition number bound is obtained for three dimensional problems these bounds are shown to be independent of coefficient jumps in the subdomain partition numerical results are also included to show the performance of the algorithm

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

discontinuous hp finite element methods for advection diffusion reaction problems we consider the hp version of the discontinuous galerkin finite element method dgfem for second order partial differential equations with nonnegative characteristic form this class of equations includes second order elliptic and parabolic equations advection reaction equations as well as problems of mixed hyperbolic elliptic parabolic type our main concern is the error analysis of the method in the absence of streamline diffusion stabilization in the hyperbolic case an hp optimal error bound is derived here we consider only advection reaction problems which satisfy a certain standard positivity condition in the self adjoint elliptic case an error bound that is h optimal and p suboptimal by frac 1 2 a power of p is obtained these estimates are then combined to deduce an error bound in the general case for elementwise analytic solutions the method exhibits exponential rates of convergence under p refinement the theoretical results are illustrated by numerical experiments

an interface strip domain decomposition preconditioner in this paper we consider domain decomposition preconditioners based on a vertex oriented vo decomposition of the computational domain in element oriented eo decompositions each element of the grid belongs to a different domain while in vo decompositions each vertex belongs to a different subdomain based on vo decompositions we present some preconditioners for the solution of the original system as well as for that of the schur complement system theoretical properties are investigated for a finite element approximation of an elliptic problem numerical results and comparison with state of the art preconditioners are also reported the numerical results presented here show the effectiveness of the proposed preconditioners and their good scalability properties

brief paper lyapunov tools for predictor feedbacks for delay systems inverse optimality and robustness to delay mismatch we consider lti finite dimensional completely controllable but possibly open loop unstable plants with arbitrarily long actuator delay and the corresponding predictor based feedback for delay compensation we study the problem of inverse optimal re design of the predictor based feedback law we obtain a simple modification of the basic predictor based controller which employs a low pass filter and has been proposed previously by mondie and michiels for achieving robustness to discretization of the integral term in the predictor feedback law the key element in our work is the employment of an infinite dimensional backstepping transformation and the resulting lyapunov function for the infinite dimensional systems consisting of the state of the ode plant and the delay state the lyapunov function allows us to quantify the lyapunov stability properties under the modified feedback the inverse optimality of the feedback and its disturbance attenuation properties for the basic predictor feedback the availability of the lyapunov function also allows us to prove robustness to small delay mismatch in both positive and negative directions

smoothed aggregation multigrid for the discontinuous galerkin method the aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems that arise from the discontinuous galerkin method the smoothed aggregation multigrid introduced by vanek for the conforming finite element method is applied to low order discretizations of convection diffusion equations for the elliptic model problem the algorithm is shown to be quasi optimal adjustments for the case of nonvanishing advection such as directionally implicit smoothing and a suitable splitting of the operator are discussed several numerical experiments are presented for two dimensional problems including a newton type linearization of the compressible navier stokes equations

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

extremum seeking for static maps with delays in this paper we address the design and analysis of multi variable extremum seeking for static maps subject to arbitrarily long time delays both gradient and newton based methods are considered multi input systems with different time delays in each individual input channel as well as output delays are dealt with the phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation based averaging based estimate of the hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point even in the presence of delays the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the time delay in particular a new backstepping like transformation is introduced to design the predictor for the gradient based extremum seeking scheme with multiple and distinct input delays the proposed newton based extremum seeking approach removes the dependence of the convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable as in the literature free of delays a source seeking example illustrates the performance of the proposed delay compensated extremum seeking schemes

multigrid methods for saddle point problems darcy systems we design and analyze multigrid methods for the saddle point problems resulting from raviart thomas nedelec mixed finite element methods for the darcy system in porous media flow uniform convergence of the w cycle algorithm in a nonstandard energy norm is established extensions to general second order elliptic problems are also addressed

two level additive schwarz methods for a discontinuous galerkin approximation of second order elliptic problems we present some two level nonoverlapping and overlapping additive schwarz methods for a discontinuous galerkin method for solving second order elliptic problems it is shown that the condition numbers of the preconditioned systems are of the order o frac h h for the nonoverlapping schwarz methods and of the order o frac h delta for the overlapping schwarz methods where h and h stand for the fine mesh size and the coarse mesh size respectively and delta denotes the size of the overlaps between subdomains numerical experiments are provided to gauge the efficiency of the methods and to validate the theory

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

two level additive schwarz preconditioners for c 0 interior penalty methods we study two level additive schwarz preconditioners that can be used in the iterative solution of the discrete problems resulting from c0 interior penalty methods for fourth order elliptic boundary value problems we show that the condition number of the preconditioned system is bounded by c 1 h3 3 where h is the typical diameter of a subdomain measures the overlap among the subdomains and the positive constant c is independent of the mesh sizes and the number of subdomains

a limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials a sequence of independent experiments is performed each one producing a letter from a given alphabet we study the number of overlapping appearances of a given pattern of letters and we prove that under quite general conditions the number of overlapping appearances of long patterns is approximately distributed according to a polya aeppli distribution

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

multigrid methods for saddle point problems oseen system abstract we develop and analyze multigrid methods for the oseen system in fluid flow we show that the w cycle algorithm is a uniform contraction if the number of smoothing steps is sufficiently large numerical results that illustrate the performance of the methods are also presented

a feti dp preconditioner for a composite finite element and discontinuous galerkin method in this paper a nitsche type discretization based on a discontinuous galerkin dg method for an elliptic two dimensional problem with discontinuous coefficients is considered the problem is posed on a polygonal region omega which is a union of n disjoint polygonal subdomains omega i of diameter o h i the discontinuities of the coefficients possibly very large are assumed to occur only across the subdomain interfaces partial omega i inside each subdomain a conforming finite element space on a quasi uniform triangulation with mesh size o h i is introduced to handle the nonmatching meshes across the subdomain interfaces a dg discretization is applied only on the interfaces for solving the resulting discrete system a feti dp type method is proposed and analyzed it is established that the condition number of the preconditioned linear system is estimated by c 1 max i log h i h i 2 with a constant c independent of h i h i h j h i and the jumps of coefficients the

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

an adaptive smith controller for time delay systems with relative degree n 2 abstract this paper addresses the control of time delay systems whose relative degree does not exceed two an adaptive smith controller together with an adaptive law similar to the delay free case is proposed by using lyapunov krasovskii functionals for an appropriate model transformation of the original system semiglobal stability of the closed loop system and asymptotic convergence of the output error is established strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties robustness properties of the adaptive controller are briefly discussed

overlapping schwarz methods on unstructured meshes using non matching coarse grids we consider two level overlapping schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions standard finite element interpolation from the coarse to the fine grid may be used our theory requires no assumption on the substructures that constitute the whole domain so the substructures can be of arbitrary shape and of different size the global coarse mesh is allowed to be non nested to the fine grid on which the discrete problem is to be solved and neither the coarse mesh nor the fine mesh need be quasi uniform in addition the domains defined by the fine and coarse grid need not be identical the one important constraint is that the closure of the coarse grid must cover any portion of the fine grid boundary for which neumann boundary conditions are given in this general setting our algorithms have the same optimal convergence rate as the usual two level overlapping domain decomposition methods on structured meshes the condition number of the preconditioned system depends only on the possibly small overlap of the substructures and the size of the coarse grid but is independent of the sizes of the subdomains

on the longest run of coincidences consider the rectangles of the first k n lines of length n in the right upper integer lattice and suppose that its points are labelled randomly by the numbers 1 2 m the time i is called coincidence if the points i 1 i 2 i k n are labelled identically asymptotic properties of the longest run of coincidences are discussed under different conditions on k n

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

norm preconditioners for discontinuous galerkin hp finite element methods we consider a norm preconditioning approach for the solution of discontinuous galerkin finite element discretizations of second order partial differential equations with a nonnegative characteristic form our solution method is a norm preconditioned three term gmres routine we find that for symmetric positive definite diffusivity tensors the convergence of our solver is independent of discretization while for the semidefinite case both theory and experiment indicate dependence on both h and p numerical results are included to illustrate performance on several test cases

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

poisson convergence for dissociated statistics summary a poisson limit theorem is derived for the number of large values observed among comparisons of independent but not necessarily identically distributed random variables the comparisons made need not be the same and may depend on the two variables being compared an application to the assessment of large numbers of correlation coefficients is given

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

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

an overlapping domain decomposition preconditioner for a class of discontinuous galerkin approximations of advection diffusion problems we consider a scalar advection diffusion problem and a recently proposed discontinuous galerkin approximation which employs discontinuous finite element spaces and suitable bilinear forms containing interface terms that ensure consistency for the corresponding sparse non symmetric linear system we propose and study an additive two level overlapping schwarz preconditioner consisting of a coarse problem on a coarse triangulation and local solvers associated to suitable problems defined on a family of subdomains this is a generalization of the corresponding overlapping method for approximations on continuous finite element spaces related to the lack of continuity of our approximation spaces some interesting new features arise in our generalization which have no analog in the conforming case we prove an upper bound for the number of iterations obtained by using this preconditioner with gmres which is independent of the number of degrees of freedom of the original problem and the number of subdomains the performance of the method is illustrated by several numerical experiments for different test problems using linear finite elements in two dimensions

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy