observability of structured linear systems in descriptor form a graph theoretic approach this paper deals with the right hand side observability of structured linear systems in descriptor form the method we propose is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are square underdetermined or overdetermined after defining digraphs which represent such systems we express in graphic terms necessary and sufficient conditions to achieve the observability of the whole or of a given part of the state these conditions are easy to check because they are based on comparison of integers and on finding edges and subgraphs in a digraph therefore our approach is suited to study large scale and or uncertain systems

system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

existence of non impulsive unique solution and stability for continuous time linear rectangular descriptor markov jump systems abstract this paper investigates the existence of non impulsive unique solution and stochastic stability problems for the continuous time linear rectangular descriptor markov jump systems dmjss at two cases for every case the sufficient and necessary conditions in terms of strict linear matrix inequalities lmis are eventually proposed to guarantee that the continuous time linear dmjss are column row regular column row impulse free stochastically stable and have a unique solution in addition with some assumptions satisfied the conditions obtained in this paper can simultaneously ensure that there is no impulse in the solution at the instant when the markov process jumps finally two examples are provided to demonstrate the effectiveness of the results

dynamic earthquake rupture simulations on nonplanar faults embedded in 3d geometrically complex heterogeneous elastic solids dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes the conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws the corresponding initial boundary value problems are both numerically and computationally challenging in addition seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault therefore reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods we present a high order accurate finite difference method for a enforcing nonlinear friction laws in a consistent and provably stable manner suitable for efficient explicit time integration b dynamic propagation of earthquake ruptures along nonplanar faults and c accurate propagation of seismic waves in heterogeneous media with free surface topography we solve the first order form of the 3d elastic wave equation on a boundary conforming curvilinear mesh in terms of particle velocities and stresses that are collocated in space and time using summation by parts sbp finite difference operators in space boundary and interface conditions are imposed weakly using penalties by deriving semi discrete energy estimates analogous to the continuous energy estimates we prove numerical stability the finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries however the method is applicable to any spatial operator with a diagonal norm satisfying the sbp property time stepping is performed with a 4th order accurate explicit low storage runge kutta scheme thus yielding a globally fourth order accurate method in both space and time we show numerical simulations on band limited self similar fractal faults revealing the complexity of rupture dynamics on rough faults

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

boundary conditions and stability of a perfectly matched layer for the elastic wave equation in first order form in computations it is now common to surround artificial boundaries of a computational domain with a perfectly matched layer pml of finite thickness in order to prevent artificially reflected waves from contaminating a numerical simulation unfortunately the pml does not give us an indication about appropriate boundary conditions needed to close the edges of the pml or how those boundary conditions should be enforced in a numerical setting terminating the pml with an inappropriate boundary condition or an unstable numerical boundary procedure can lead to exponential growth in the pml which will eventually destroy the accuracy of a numerical simulation everywhere in this paper we analyze the stability and the well posedness of boundary conditions terminating the pml for the elastic wave equation in first order form first we consider a vertical modal pml truncating a two space dimensional computational domain in the horizontal direction we freeze all coefficients and consider a left half plane problem with linear boundary conditions terminating the pml the normal mode analysis is used to study the stability and well posedness of the resulting initial boundary value problem ibvp the result is that any linear well posed boundary condition yielding an energy estimate for the elastic wave equation without the pml will also lead to a well posed ibvp for the pml second we extend the analysis to the pml corner region where both a horizontal and vertical pml are simultaneously active the challenge lies in constructing accurate and stable numerical approximations for the pml and the boundary conditions third we develop a high order accurate finite difference approximation of the pml subject to the boundary conditions to enable accurate and stable numerical boundary treatments for the pml we construct continuous energy estimates in the laplace space for a one space dimensional problem and two space dimensional pml corner problem we use summation by parts finite difference operators to approximate the spatial derivatives and impose boundary conditions weakly using penalties in order to ensure numerical stability of the discrete pml it is necessary to extend the numerical boundary procedure to the auxiliary differential equations this is crucial for deriving discrete energy estimates analogous to the continuous energy estimates numerical experiments are presented corroborating the theoretical results moreover in order to ensure longtime numerical stability the boundary condition closing the pml or its corresponding discrete implementation must be dissipative furthermore the numerical experiments demonstrate the stable and robust treatment of pml corners

solvability conditions consistency and weak consistency for linear differential algebraic equations and time invariant singular systems the general case we present several solvability concepts for linear differential algebraic equations daes with constant coefficients on the positive time axis as well as for the associated singular systems and investigate under which conditions these concepts are met next we derive necessary and sufficient conditions for global consistency of initial conditions for the dae as well as for the system and generalize these conditions with respect to our concept of weak consistency our distributional approach enables us to generalize results in an earlier paper where singular systems are assumed to have a regular pencil in the sense of gantmacher in particular we establish that global weak consistency in the system sense is equivalent to impulse controllability

sbp sat finite difference discretization of acoustic wave equations on staggered block wise uniform grids abstract we consider the numerical simulation of the acoustic wave equations arising from seismic applications for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency we relax the uniform grid restriction on finite difference methods and allow the grids to be block wise uniform with nonconforming interfaces in doing so variations in the wave speeds of the subterranean media can be accounted for more efficiently staggered grid finite difference operators satisfying the summation by parts sbp property are devised to approximate the spatial derivatives appearing in the acoustic wave equation these operators are applied within each block independently the coupling between blocks is achieved through simultaneous approximation terms sats which impose the interface conditions weakly i e by penalty ratio of the grid spacing of neighboring blocks is allowed to be rational number for which specially designed interpolation formulas are presented these interpolation formulas constitute key pieces of the simultaneous approximation terms the overall discretization is shown to be energy conserving and examined on test cases of both theoretical and practical interests delivering accurate and stable simulation results

observer design for descriptor systems two detectability notions are introduced for the most general class of linear descriptor systems necessary and sufficient conditions are derived for the detectabilities and for the existence of observers depending on existence conditions satisfied the observers can be either in the familiar luenberger form or in a generalized form i e in descriptor form as the original system itself is a unified procedure is provided for the design of observers in both forms

observability of singular systems with commensurate time delays and neutral terms this paper deals with the observability problem of a sort of singular systems with commensurate time delays in the trajectories of the system in the time derivative of the trajectories neutral terms and in the output system by using a recursive algorithm sufficient conditions easy testable are proposed for guaranteeing the backward and the algebraic observability of the system this condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

a nonlinear luenberger like observer for nonlinear singular systems this paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs we firstly regularize the singular system by injecting the derivative of outputs into the system then differential geometric method is applied to transform the regularized system into a simple normal form for which a luenberger like observer is proposed

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

causal observability of descriptor systems observability analysis for descriptor systems by using a matrix pencil approach is presented systems under consideration are the most general class of linear continuous descriptor systems a few practically relevant notions of observability particularly the causal observability which corresponds to the existence of a luenberger observer and the corresponding necessary and sufficient test conditions are provided the interpretation of various observabilities in terms of matrix pencils offers insights into the physical meaning of these concepts

simultaneous state and input reachability for linear time invariant systems abstract in this paper we give an explicit solution to the behavioral reachability problem for linear time invariant systems which amounts to finding an explicit control law that reaches a given final input state pair u 1 x 1 in a given finite time t 1 we first tackle the case of state space realizations and we then extend the obtained results to the case of implicit realizations for this we use the geometric approach and some results of the viability theory some complements are given about the existing relationships between reachability and pole placement as well as some notions of unicity and existence of solution

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

application of the multiaxial perfectly matched layer m pml to near surface seismic modeling with rayleigh waves perfectly matched layer pml absorbing boundaries are widely used to suppress spurious edge reflections in seismic modeling when modeling rayleigh waves with the existence of the free surface the classical pml algorithm becomes unstable when the poisson s ratio of the medium is high numerical errors can accumulate exponentially and terminate the simulation due to computational overflows numerical tests show that the divergence speed of the classical pml has a nonlinear relationship with the poisson s ratio generally the higher the poisson s ratio the faster the classical pml diverges the multiaxial pml m pml attenuates the waves in pmls using different damping profiles that are proportional to each other in orthogonal directions the proportion coefficients of the damping profiles usually vary with the specific model settings if they are set appropriately the m pml algorithm is stable for high poisson s ratio earth models through numerical tests of 40 models with poisson s ratios that varied from 0 10 to 0 49 we found that a constant proportion coefficient of 1 0 for the x and z directional damping profiles is sufficient to stabilize the m pml for all 2d isotropic elastic cases wavefield simulations indicate that the instability of the classical pml is strongly related to the wave phenomena near the free surface when applying the multiaxial technique only in the corners of the pml near the free surface the original m pml technique can be simplified without losing its stability the simplified m pml works efficiently for homogeneous and heterogeneous earth models with high poisson s ratios the analysis in this paper is based on 2d finite difference modeling in the time domain that can easily be extended into the 3d domain with other numerical methods

the role of numerical boundary procedures in the stability of perfectly matched layers in this paper we address the temporal energy growth associated with numerical approximations of the perfectly matched layer pml for maxwell s equations in first order form in the literature several studies have shown that a numerical method which is stable in the absence of the pml can become unstable when the pml is introduced we demonstrate in this paper that this instability can be directly related to numerical treatment of boundary conditions in the pml first at the continuous level we establish the stability of the constant coefficient initial boundary value problem for the pml to enable the construction of stable numerical boundary procedures we derive energy estimates for the pml in the laplace space second we develop a high order accurate and stable numerical approximation for the pml using summation by parts finite difference operators to approximate spatial derivatives and weak enforcement of boundary conditions using penalties by constructing analogous discrete energy estimates we

time domain solution to descriptor variable systems the time domain solution to the fast subsystem of the descriptor variable system of the form ex spl dot ax bu with e singular is given by laplace inverse transformation a new and significant feature of the solution is that it contains impulse terms excited by the values of sufficiently smooth input u and its derivatives at the initial time point based on the solution the notions of consistent initial conditions classical solutions and impulse free solutions are discussed perfectly the impulse controllability is discussed also which admits the same interpretation as the controllability at infinity in frequency domain

brief paper jump modes analysis and observer design for discrete singular systems this paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems the notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied the effect of jump modes on the existence of reduced order normal luenberger observers for discrete singular systems is investigated necessary and sufficient conditions for the existence of normal luenberger observers and the corresponding observer design procedure are obtained

boundary waves and stability of the perfectly matched layer for the two space dimensional elastic wave equation in second order form boundary waves and stability of the perfectly matched layer for the two space dimensional elastic wave equation in second order form

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

vertex algebras and the cohomology ring structure of hilbert schemes of points on surfaces using vertex algebra techniques we determine a set of generators for the cohomology ring of the hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

boundary estimates for the elastic wave equation in almost incompressible materials we study the half plane problem for the elastic wave equation subject to a free surface boundary condition with particular emphasis on almost incompressible materials a normal mode analysis is developed to estimate the solution in terms of the boundary data showing that the problem is boundary stable the dependence on the material properties which is difficult to analyze by the energy method is made transparent by our estimates the normal mode technique is used to analyze the influence of truncation errors in a finite difference approximation our analysis explains why the number of grid points per wave length must be increased when the shear modulus mu becomes small compared to the first lame parameter lambda that is for almost incompressible materials when the surface waves are scaled to have unit wave length our analysis predicts that the grid size must be proportional to mu lambda 1 2 for a second order method for a fourth order method the grid size can be proportional t

error bounded schemes for time dependent hyperbolic problems in this paper we address the error growth in time for hyperbolic problems in first order form in bounded domains the energy method is used to study when an error growth or a fixed error bound is obtained it is shown that the choice of boundary procedure is a crucial point numerical experiments corroborate the theoretical findings

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

remarks on observability of implicit linear discrete time systems abstract some results concerning the observability of implicit linear discrete time systems of the form exk 1 fxk yk hxk are presented it is not assumed that the corresponding pencil se f is regular the concept of reachability with pulse introduced in this paper is shown to be dual to the notion of observability

existence of nonimpulsive unique solution and stability for discrete time linear rectangular descriptor markov jump systems this paper investigates the existence of nonimpulsive unique solution and stochastic stability problems for the discrete time linear rectangular descriptor markov jump systems at two cases for every case the sufficient and necessary conditions in terms of strict linear matrix inequalities are eventually proposed to guarantee that the discrete time linear rectangular descriptor markov jump systems are column row regular column row causal stochastically stable and have a unique solution in addition some assumptions are introduced to ensure that there is no impulse in the solution at the instant when the markov process jumps moreover the concrete procedures on how to apply the results obtained in this paper are presented as well finally an example is provided to demonstrate the effectiveness of the results

observability and detectability of singular linear systems with unknown inputs in this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled the case when the matrix pencil is non regular is comprised i e more than one solution for the differential equation is allowed it is shown that under suitable assumptions the original problem can be studied by means of a regular non singular linear system with unknown inputs and algebraic constraints thus it is shown that for purposes of analysis the algebraic equations can be included as part of an extended system output based on this analysis we obtain necessary and sufficient conditions guaranteeing the observability or detectability of the system in terms of the zeros of the system matrix corresponding algebraic conditions are given in order to test the observability and detectability a formula is provided that expresses the state as high order derivative of a function of the output which allows for the reconstruction of the actual state vector it is shown that the unknown inputs may be reconstructed also

observability of linear discrete time systems of algebraic and difference equations abstractthe notion of observability for higher order discrete time systems of algebraic and difference equations is studied such systems are also known as polynomial matrix descriptions attention is first given to a special form of descriptor systems with a state lead in the output this system is transformed into its causal and noncausal subsystems and observability criteria are given in terms of the subsystem s matrices and the fundamental matrix sequence of the matrix pencil e a afterwards the higher order system is studied by transforming it into a first order descriptor system of the above form an observability criterion is provided for the higher order system in terms of the laurent expansion at infinity of the system s polynomial matrix in addition observability is connected with the coprimeness of the polynomial matrices of the higher order system and the coprimeness of the matrix pencils of the descriptor system

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

controllability and elimination of impulsive modes in descriptor systems as a refined notion impulsive mode controllability is suggested for the general class of linear continuous descriptor systems this notion reveals rich properties of the general descriptor systems in terms of admissibility of initial conditions admissibility of feedback control and impulsive mode elimination the condition for impulsive mode controllability is derived and proved to be necessary and sufficient for the existence of admissible feedback controls eliminating impulsive modes under impulsive mode controllability admissible feedback controls are constructed for eliminating impulsive modes on the basis of numerically reliable decompositions of the system s coefficient matrices

a stable discontinuous galerkin method for the perfectly matched layer for elastodynamics in first order form we present a stable discontinuous galerkin dg method with a perfectly matched layer pml for three and two space dimensional linear elastodynamics in velocity stress formulation subject to well posed linear boundary conditions first we consider the elastodynamics equation in a cuboidal domain and derive an unsplit pml truncating the domain using complex coordinate stretching the hyperbolic structure of the underlying system enables the construction of continuous energy estimates in the time domain for the elastic wave equation and in the laplace space for a sequence of pml model problems with variations in one two and three space dimensions respectively they correspond to pmls normal to boundary faces along edges and in corners second we develop a dg numerical method for the linear elastodynamics equation using physically motivated numerical flux and penalty parameters which are compatible with all well posed internal and external boundary conditions when the pml damping vanishes in all directions by construction our choice of penalty parameters yield an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate third to ensure numerical stability of the discretization when pml damping is present it is necessary to extend the numerical dg fluxes and the numerical inter element and boundary procedures to the pml auxiliary differential equations this is crucial for deriving discrete energy estimates analogous to the continuous energy estimates numerical solutions are evolved in time using the high order arbitrary derivative ader time stepping scheme of the same order of accuracy with the spatial discretization by combining the dg spatial approximation with the high order ader time stepping scheme and the accuracy of the pml we obtain an arbitrarily high order accurate wave propagation solver in the time domain numerical experiments are presented in two and three space dimensions corroborating the theoretical results

some generalized notions of observability generalized state space systems are a more natural way of describing dynamical behavior than standard state space systems such systems exhibit a much richer observability structure than standard state space systems three notions of observability are defined for generalized state space systems in contrast to previous work regularity is not assumed geometric characterization of each type of observability and matrix rank tests for each type of observability are derived

disturbance impulse controllability in descriptor system the descriptor system ex ax gu hv with external disturbance v is considered to characterize the possibility to cancel the impulses produced by external disturbance v through using control u the concept of disturbance impulse controllability is introduced

a stable penalty method for the compressible navier stokes equations i open boundary conditions the purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible navier stokes equations in three spatial dimensions the treatment uses the conservation form of the navier stokes equations and utilizes linearization and localization at the boundaries based on these variables the proposed boundary conditions are applied through a penalty procedure thus ensuring correct behavior of the scheme as the reynolds number tends to infinity the versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

unknown input functional observability of descriptor systems with neutral and distributed delay effects in this paper a general class of linear systems with time delays is considered which includes linear classical systems linear systems with commensurate delays neutral systems and singular systems with delays after given a formal definition of functional backward observability bo an easily testable condition is found the fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives the methodology we follow consists in an iterative algorithm based upon the classical silverman algorithm used for inversion of linear systems by using basic module theory we manage to prove that the proposed algorithm is convergent a direct application of studying functional observability is that a condition can be derived for systems with distributed delays also we do this as a case of study the obtained results are illustrated by two examples one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

singular lq problem for nonregular descriptor systems in this paper a singular linear quadratic lq problem for non regular descriptor systems is investigated under some general conditions the optimal control and the optimal state of the lq problem are given the optimal control is synthesized as state feedback all the finite eigenvalues of the closed loop system are located on the left half complex plane the state of the closed loop system has the least free entries

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

analysis of impulsive modes and luenberger observers for descriptor systems abstract in this paper the distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time invariant descriptor systems it reveals that the input generatable impulsive modes are very crucial to the existence of normal luenberger observers of the systems based on this observation an earlier known concept called strongly detectability for regular descriptor systems is extended to irregular case that is shown to be of much clearer physical meanings in classical sense than a recently proposed equivalent notion of causal detectability does thus similar to the regular case strong detectability is also a sufficient and necessary condition for the existence of normal luenberger observers of irregular descriptor systems

brief paper observability analysis and sensor location study for structured linear systems in descriptor form with unknown inputs this paper deals with the state and input right hand side observability and the sensor location problem to ensure this property for structured linear systems in the descriptor form the proposed method is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are underdetermined overdetermined or square after defining a bipartite graph which represents such systems we deduce some graphic necessary and sufficient conditions to achieve the right hand side observability of the state and the input next we propose a sensor placement procedure to recover this property more precisely we provide the minimal number of the sensors required and either their pertinent location or a necessary and sufficient condition to check if a given sensor configuration is adequate or not to ensure state and input right hand side observability our approach uses algorithms with polynomial complexity orders and assumes only the knowledge of the system s structure and so is suited for large scale systems

on observers for nonlinear differential algebraic systems we extend a recent approach to observer design for linear differential algebraic systems to systems with lipschitz nonlinearities the observer design further extends the standard luenberger type observer design we show that the design parameters for the observer can be obtained by the solution of a riccati type inequality the solutions of the latter can in turn be obtained by solving a set of linear matrix inequalities lmis and bilinear matrix inequalities bmis which provides a computational procedure a feature of the presented observer design is the possibility of reformulation as an ordinary differential equation

chern classes of tautological sheaves on hilbert schemes of points on surfaces we give an algorithmic description of the action of the chern classes of tautological bundles on the cohomology of hilbert schemes of points on a smooth surface within the framework of nakajima s oscillator algebra this leads to an identification of the cohomology ring of hilb n a2 with a ring of explicitly given differential operators on a fock space we end with the computation of the top segre classes of tautological bundles associated to line bundles on hilb n up to n 7 extending computations of severi lebarz tikhomirov and troshina and give a conjecture for the generating series

optimal time splitting for two and three dimensional navier stokes equations with mixed derivatives a new explicit time splitting algorithm has been developed for finite difference modelling of the full two and three dimensional time dependent compressible viscous navier stokes equations of fluid mechanics the scheme is optimal in the sense that the split operators achieve their maximum allowable time step i e the corresponding courant number the algorithm allows a conservation form formulation stability is proven analytically and verified numerically in proving stability it was shown that all nine matrix coefficients of the navier stokes equations are simultaneously symmetrizable by a similarity transformation two such transformations and their resulting symmetric matrix coefficients are presented explicitly

a skew symmetric discontinuous galerkin spectral element discretization and its relation to sbp sat finite difference methods this paper shows that the discontinuous galerkin collocation spectral element method with gauss lobatto points dgsem gl satisfies the discrete summation by parts sbp property and can thus be classified as an sbp sat simultaneous approximation term scheme with a diagonal norm operator in the same way sbp sat finite difference schemes can be interpreted as discontinuous galerkin type methods with a corresponding weak formulation based on an inner product formulation common in the finite element community this relation allows the use of matrix vector notation common in the sbp sat finite difference community to show discrete conservation for the split operator formulation of scalar nonlinear conservation laws for dgsem gl and diagonal norm sbp sat based on this result a skew symmetric energy stable discretely conservative dgsem gl formulation applicable to general diagonal norm sbp sat schemes for the nonlinear burgers equation is constructed