stability robustness of linear state space models with structured perturbations abstract a new approach is proposed to analyze the stability robustness of linear state space models under structured uncertainties the presented method is computationally simple to use and can be calculated easily by computer the merit of the proposed method is demonstrated by two examples where the results achieved are much better than those already obtained by the lyapunov stability method and the transition matrix approach

nilmanifolds of dimension 8 admitting anosov diffeomorphisms after more than thirty years the only known examples of anosov diffeomorphisms are topologically conjugated to hyperbolic automorphisms of infranilmanifolds and even the existence of an anosov automorphism is a really strong condition on an infranilmanifold any anosov automorphism determines an automorphism of the rational lie algebra determined by the lattice which is hyperbolic and unimodular and conversely these two conditions together are strong enough to make of such rational nilpotent lie algebras called anosov lie algebras very distinguished objects in this paper we classify anosov lie algebras of dimension less than or equal to 8 as a corollary we obtain that if an infranilmanifold of dimension n 8 admits an anosov diffeomorphism f and it is not a torus or a compact flat manifold i e covered by a torus then n 6 or 8 and the signature of f necessarily equals 3 3 or 4 4 respectively

passivity based sliding mode control of uncertain singular markovian jump systems with time varying delay and nonlinear perturbations in this paper a sliding mode control smc with passivity of uncertain singular markovian jump systems smjs with time varying delay and nonlinear perturbations is investigated firstly a new integral type switching surface is designed secondly by introducing free matrix method and lyapunov functionals a delay dependent sufficient condition in terms of strict linear matrix inequalities lmi is derived for the resulting sliding mode dynamics such that the closed loop system is stochastically admissible and robustly passive for all admissible uncertainties thirdly a smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally numerical examples are provided to demonstrate the effectiveness of the proposed method

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

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

asymptotic behaviour of solutions of systems of discrete equations via liapunov type technique abstract the second liapunov method serves as a powerful tool for the investigation of the stability of the trivial solution of ordinary differential equations systems and discrete equations systems in the presented paper a liapunov type qualitative approach is used for the investigation of asymptotic behaviour of the solutions of systems of discrete equations conditions for the existence of continuum of solutions the graphs of which remain within a given prescribed set are formulated for the general systems of discrete equations u k f k u k an additional advantage of the presented approach consists of the fact that no assumption concerning the existence of the trivial solution or the existence of an equilibrium point of systems considered is assumed moreover the asymptotic behaviour of solutions of some classes of linear difference systems is given by means of concrete asymptotic formulae several illustrative examples are considered too

a quantitative study on the stability of quadratic delay difference systems this paper estimates the size of the stability region around zero for quadratic delay difference systems when the initial disturbance is in the asymptotic stability region the solution of the initial value problem of the quadratic delay difference system approaches zero examples are given for a three dimensional system and three one dimensional equations to demonstrate both stability and instability examples 2 4 show that when parameters in the systems do not satisfy the stability conditions the zero solutions can be unstable three evolution features of initial disturbances are shown numerically decaying to zero being amplified but bounded and growing to infinity example 3 further shows that the stable zero solution may not be a global attractor numerical results confirm the conclusions of the main theorem in this paper and imply that our estimation of the size of the stability region are of reasonable accuracy 1998 elsevier science ltd all rights reserved

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

robust control for linear systems with structured state space uncertainty abstract a recent sufficient condition for the stability robustness of linear systems with time varying norm bounded state space uncertainty is extended to include the structure of the uncertainty our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix therefore this robustness result is especially well suited to the design of control systems using eigenstructure assignment when the uncertainty is time invariant our norm is also an upper bound on the incremental eigenvalue perturbations we also consider the use of perron weightings to reduce conservatism and the extension of the results to discrete time systems

some two step and three step nilpotent lie groups with small automorphism groups we construct examples of two step and three step nilpotent lie groups whose automorphism groups are small in the sense of either not having a dense orbit for the action on the lie group or being nilpotent the latter being stronger from the results we also get new examples of compact manifolds covered by two step simply connected nilpotent lie groups which do not admit anosov automorphisms

parameter identification using mollification for predator prey models in spatially heterogeneous environments a stable numerical method is introduced for the identification of population densitiesand spatially dependent diffusion coefficients in a lotka volterra predator prey model in which bias dispersal is present in this problem noisy data at the active boundary and initial measured population densities are given this algorithm makes no assumption on the amount and or character of the noise in the data

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

einstein solvmanifolds existence and non existence questions the aim of this paper is to study the problem of which solvable lie groups admit an einstein left invariant metric the space mathcal n of all nilpotent lie brackets on mathbb r n parametrizes a set of n 1 dimensional rank one solvmanifolds s mu mu in mathcal n containing the set of all those which are einstein in that dimension the moment map for the natural gl n action on mathcal n evaluated at mu in mathcal n encodes geometric information on s and suggests the use of strong results from geometric invariant theory for instance the functional on mathcal n whose critical points are precisely the einstein s s is the square norm of this moment map we use a gl n invariant stratification for the space mathcal n and show that there is a strong interplay between the strata and the einstein condition on the solvmanifolds s as an application we obtain criteria to decide whether a given nilpotent lie algebra can be the nilradical of a rank one einstein solvmanifold or not we find several examples of mathbb n graded even 2 step nilpotent lie algebras which are not a classification in the 7 dimensional 6 step case and an existence result for certain 2 step algebras associated to graphs are also given

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

pole placement and compensator design of generalized systems abstract the system considered is a generalized system e ax bu y cx with matrix e singular when the impulsive modes of the system are both controllable and observable it is shown in this paper that these modes can be eliminated by almost any constant output feedback for a strongly controllable and observable generalized system after its impulsive modes are eliminated the poles of the system can be assigned arbitrarily by state feedback even if the states are not available the paper adopts an efficient method to design a compensator for the system

parameter estimation for a drying system in a porous medium we introduce a stable numerical method for the recovery of the temperature and moisture distributions in a liukov system with space dependent diffusion coefficients in this problem only cauchy noisy data at the active boundary is given and no information about the amount and or character of the noise in the data is assumed the error analysis for the algorithm is discussed and a numerical example is presented

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

homogeneous indices feedback invariants and control structure theorem for generalized linear systems we define a new set of indices for a generalized linear system these indices referred to as the homogeneous indices are a natural generalization of the minimal column indices kronecker indices of an ordinary state space system we prove that the homogeneous indices are a complete set of invariants for the action of a natural group of feedback transformations on generalized linear systems we also show that the homogeneous indices determine exactly which closed loop invariant polynomials can be assigned by feedback thereby generalizing the control structure theorem of rosenbrock

robustness of regional pole placement for uncertain continuous time implicit systems in this note under assumptions that the nominal linear implicit system is regular impulse free with all its generalized eigenvalues lying inside some specified regions sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices

state feedback and transfer matrix in singular systems abstract the influence of state feedback on the transfer matrix in singular systems is considered we first discuss the problem for siso systems then by utilizing the time scale transformation the same problem is solved for mimo systems we also consider realizations of the feedback control strategies given here it is pointed out that the singular system is distinguished from the normal one by an important feature we can design a pure input prediction system for it finally the results are applied to the model matching problem

robust stability of state space models with structured uncertainties a method for robust eigenvalue location analysis of linear state space models affected by structured real parametric perturbations is proposed the approach based on algebraic matrix properties deals with state space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters a method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed the method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space this problem which can be reduced to finding the real solutions of a system of polynomial equations simplifies considerably when cases with one or two uncertain parameters are considered for these cases necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems

fundamental properties of the manifold of singular and regular linear systems abstract we construct a real analytic manifold l of systems of the form e x ax bu y cx and show that l is the completion with respect to solutions of the set of regular state space systems i e those systems with nonsingular e other geometric and analytic properties of l are established including genericity of the regular systems

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

fundamental theorem of state feedback for singular systems abstract the limits of state feedback in altering the dynamics of singular systems are studied a necessary and sufficient condition is given for a list of polynomials to be invariant polynomials of a proper system obtained by state feedback from the singular system the condition consists of inequalities which involve the controllability indices of the singular system and the degrees of the invariant polynomials the development is based on the properties of polynomial matrices a procedure is given for the calculation of a feedback gain which achieves the desired dynamics

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

anosov automorphisms on compact nilmanifolds associated with graphs we associate with each graph s e a 2 step simply connected nilpotent lie group n and a lattice in n we determine the group of lie automorphisms of n and apply the result to describe a necessary and sufficient condition in terms of the graph for the compact nilmanifold n f to admit an anosov automorphism using the criterion we obtain new examples of compact nilmanifolds admitting anosov automorphisms and conclude that for every n 17 there exist a n dimensional 2 step simply connected nilpotent lie group n which is indecomposable not a direct product of lower dimensional nilpotent lie groups and a lattice in n such that n f admits an anosov automorphism we give also a lower bound on the number of mutually nonisomorphic lie groups n of a given dimension satisfying the condition necessary and sufficient conditions are also described for a compact nilmanifold as above to admit ergodic automorphisms

robust stability and robust pole assignment of linear systems with structured uncertainty sufficient conditions for the robust stability of linear time varying systems are presented the stability criteria are extended to the problem of the robust pole assignment of linear time invariant systems to a specified region these criteria both for robust stability and robust pole assignment improve some results in the literature examples are given to demonstrate the new criteria

fourier truncation method for high order numerical derivatives we consider a classical ill posed problem numerical differentiation with a new method we propose fourier truncation method to compute high order numerical derivatives a holder type stability estimate is obtained a numerical implementation is described numerical examples show that the proposed method is effective and stable

stability analysis and stabilization of 2 d singular roesser models abstract this paper addresses the problem of controller design for 2 d singular roesser models sufficient stability conditions are formulated in terms of strict linear matrix inequalities lmis for 2 d singular systems described by the roesser models then a set of sufficient conditions for existence of desired a state feedback controller are obtained numerical examples are provided to demonstrate the effectiveness of the proposed method

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

on the congruence transformation of a pencil of real symmetric matrices to a pencil with identical characteristic polynomial abstract simultaneous nonorthogonal congruence transformations for pairs a b of 2 2 real symmetric matrices which leave the characteristic polynomial of the pencil x 1 a x 2 b invariant are studied

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

stability of finite delay difference systems the stability of finite delay difference systems has recently been discussed in l in this paper we consider the delay difference systems with infinite delay of the following form x n 1 g n x s s 1 1 1 n g n x 1 where 1 is an integer or w we assume g n 0 0 forn l l l so that 1 has the zero solution x n 0 clearly for any given integer n l 1 and a given bounded initial function 4 l 1 1 no rk there is a unique solution of l denoted by x n n 4 such that it satisfies 1 for all integers n 2 n and x n no 4 444 forn f l l no for any integer m 2 co let 2 m m 1 i and 2 z the integer set if m a for any n e z define ii411 tlnl sup l s 15 s 5 n and for any h 0 let c n 4 z rk i nl h in the sequel we always assume that the variables n r and s take integer values and the corresponding intervals are discrete intervals

robustness of discrete systems under structured uncertainties we give a sufficient condition for the robust stability of the discrete system x k 1 f e x k where the perturbation e is bounded e u a necessary and sufficient condition is derived in the case where f is a positive or a negative matrix and u f the stability of interval matrices is also considered numerical examples are given for illustration

constructing infra nilmanifolds admitting an anosov diffeomorphism abstract in this paper we establish an algebraic characterization of those infra nilmanifolds modeled on a free c step nilpotent lie group and with an abelian holonomy group admitting an anosov diffeomorphism we also develop a new method for constructing examples of infra nilmanifolds having an anosov diffeomorphism

a quantitative study on the stability of delay discrete singular systems for quadratic delay discrete singular systems an algebraic criterion on the stability is established and the size of the uniform stability region and asymptotic stability region around zero is estimated hence the criterion is both qualitative and quantitative with the computer techniques the criterion dependent of delay is easy test and applies to the application in the practice an illustrative simulation is given to illustrate the application of the obtained result

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

an lmi approach to d stability and d stabilization of linear discrete singular systems with state delay abstract the problems of d stability and d stabilization for linear discrete singular systems with state delay are addressed in this paper by using the state augmentation technique a necessary and sufficient d stability condition and a sufficient d stabilization condition for linear discrete singular time delay systems are firstly proposed then based on these conditions quadratic d stability and d stabilization conditions for linear discrete singular time delay systems with norm bounded uncertainties and interval uncertainties are obtained respectively both the d stability and d stabilization conditions are proposed in terms of linear matrix inequalities finally illustrative examples show that the proposed conditions are effective to check the d stability and to design the d stabilizing controller for linear discrete singular time delay systems

technical communique a note on the existence of a solution and stability for lipschitz discrete time descriptor systems this paper addresses the existence and uniqueness of a solution and stability for lipschitz discrete time descriptor systems by means of the fixed point principle a criterion is presented via a matrix inequality and the criterion guarantees the existence and uniqueness of a solution in addition a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously it is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system finally the approach is illustrated by a numerical example

the linear quadratic optimal regulator for descriptor systems in this paper we investigate the linear quadratic optimal regulator problem for the continuous time descriptor system e dot x ax bu where e is in general a singular matrix we solve first a general finite horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors from this trajectory the optimal feedback gain relating the control and descriptor variable can be computed by transforming to a coordinate system which can be computed by performing a singular value decomposition of e we derive several riccati differential equations all of which have the same solution this solution gives the optimal cost the steady state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters in general there does not exist a unique optimal feedback gain but rather the gain is constrained to lie in a linear variety whose dimension is equal to the number of inputs times the rank deficiency of e

technical communique robust stabilization for uncertain discrete singular systems this paper considers the problem of robust stabilization for uncertain discrete singular systems subject to time invariant norm bounded unstructured uncertainty in the state matrix the problem we address is the design of state feedback controllers such that the resulting closed loop system is regular causal as well as stable for all admissible uncertainties in this connection the concept of generalized quadratic stabilizability is defined in terms of matrix inequalities a necessary and sufficient condition for generalized quadratic stabilizability is derived under certain assumptions when this condition holds the explicit formula of a state feedback controller solving the problem is also given the results can be viewed as extensions of existing results on robust stabilization of uncertain discrete standard state space systems

the stability robustness of generalized eigenvalues the concept of stability radius is generalized to matrix pairs a matrix pair is said to be stable if its generalized eigenvalues are located in the open left half of the complex plane the stability radius of a matrix pair a b is defined to be the norm of the smallest perturbation delta a such that a delta a b is unstable the purpose is to estimate the stability radius of a given matrix pair depending on whether the matrices under consideration are complex or real the problem can be classified into two cases the complex case is easy and a complete solution is provided the real case is more difficult and only a partial solution is given

d stability robustness for linear discrete uncertain singular systems with delayed perturbations in this paper the robust d stability problem i e the robust eigenvalue clustering in a specified circular region problem of linear discrete singular systems with both structured elemental parameter uncertainties and delayed perturbations is investigated under the assumptions that the linear discrete nominal singular system is regular and causal and has all its finite eigenvalues lying inside a specified circular region by using the maximum modulus principle and the spectral radius of matrices a new sufficient condition is proposed to preserve the assumed properties when both structured parameter uncertainties and delayed perturbations are added into the linear discrete nominal singular system when all the finite eigenvalues lie inside the unit circle of the z plane the proposed criterion will become the stability robustness criterion the proposed criterion is mathematically proved and numerically shown respectively to be less conservative than the existing ones reported recently

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

robust h control for uncertain discrete singular systems with pole placement in a disk abstract this paper addresses the design of robust h controllers for uncertain discrete singular systems with time invariant uncertainty in both the state and measurement matrices the singular system to be controlled is not assumed to be regular a regular dynamic output feedback controller is designed such that a prescribed h performance condition is satisfied and the closed loop poles are placed in a specified disk while the regularity causality and stability of the closed loop system can be guaranteed for all admissible uncertainties the desired controller can be obtained by solving a set of matrix inequalities a numerical example is given to demonstrate the application of the proposed method

a simple approach to solving the diophantine equation based on the state space concepts a simple approach to finding all polynomial matrix solutions of the diophantine equation is proposed the procedure presented is very simple in comparison to earlier ones unlike earlier ones it is not necessary to solve any equation only two constant matrices which could be selected at random are required all solutions are expressed in an explicit formula form

solvable lie algebras and graphs abstract we define a solvable extension of the graph 2 step nilpotent lie algebras of 5 by adding elements corresponding to the 3 cliques of the graph we study some of their basic properties and we prove that two such lie algebras are isomorphic if and only if their graphs are isomorphic we also briefly discuss some metric properties providing examples of homogeneous spaces with nonpositive curvature operator and solvsolitons

stability analysis of delay difference systems abstract for quadratic delay difference systems a result related to stability analysis is established more specifically the zero solution is uniformly stable and uniformly asymptotically stable for suitably small delay r where r is the admissible maximum value of delay under certain conditions furthermore the estimates of the corresponding stability and asymptotic stability regions are given hence the obtained result is both qualitative and quantitative also as a by product an improved uniform asymptotic stability criterion is established

simultaneous space diffusivity and source term reconstruction in 2d ihcp a numerical marching scheme is presented for the simultaneous recovery of the diffusivity coefficient spatial source term temperature and heat flux distributions in the two dimensional inverse heat conduction problem when noisy data at the active boundary and the initial measured temperature distribution are given no information about the quality and or quantity of the noise is assumed a proof of stability and convergence of the algorithm are provided together with several numerical examples of interest

singular systems a new approach in the time domain a new approach in the time domain is developed for the study of singular linear systems of the form e dot x ax bu y cx with e singular central to the approach is the fundamental triple alpha e a 1 e alphae a 1 b c with a real number satisfying det alpha e a neq 0 controllability and observability matrices are expressed in terms of the fundamental triple new tests for impulse controllability and impulse observability are also established feedback control problems including pole placement decoupling and disturbance localization are studied by use of a modified proportional and derivative feedback of the state in the form of u f alpha x dot x v

observers for singular systems the following three major aspects of the design of observers for linear time invariant singular systems are resolved the necessary and sufficient conditions for the problem to have a solution the order of the minimal observer and the properties of the closed loop system separation principle an algorithm is presented for the construction of the minimal order observer

robust eigenvalue clustering in a specified circular region for linear uncertain discrete singular systems with state delay in this paper the robust eigenvalue clustering in a specified circular region problem i e the robust d stability problem of linear discrete singular time delay systems with structured elemental parameter uncertainties is investigated under the assumptions that the linear nominal discrete singular time delay system is regular and causal and has all its finite eigenvalues lying inside a specified circular region a new sufficient condition is proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time delay system when all the finite eigenvalues are just required to locate inside the unit circle of the z plane the proposed criterion will become the stability robustness criterion the presented criterion is mathematically proved to be less conservative than the existing ones reported very recently in the literature

robust control analysis and design for discrete time singular systems abstract in this paper we propose a simple approach to analyse stability robustness of discrete time singular systems under structured perturbations the developed robustness criteria are then applied to solve robust regional pole assignment problems of singular systems a robust control design algorithm via state feedback is also given the robust stability problem of singular systems is more complicated than that of regular systems not only stability robustness but system regularity and impulse elimination should be considered simultaneously since the results of robust control and analysis for singular systems is not available in the literature as much as other fields the paper may be viewed as a complementary result in this field although only discrete time case is discussed several results can be directly applied to continuous time systems as well

parametric eigenstructure assignment for continuous time descriptor systems abstract eigenstructure assignment for continuous time descriptor systems ex t ax t bu t via descriptor variable feedback control u t kx t is treated a new parametric form for the gain matrix k which assigns rank e arbitrary finite eigenvalues to the closed loop system is developed this form embraces two sets of design parameter vectors characterizing respectively the assignable eigenvectors associated with the finite eigenvalues and a necessary and sufficient condition for closed loop system regularity in addition a certain submatrix of k turns out to be totally free whenever nullity e exceeds rank b unlike earlier methods the eigenvectors associated with the infinite eigenvalues are dispensed with in the solution algorithm

a survey of canonical forms and invariants for unitary similarity abstract matrices a and b are said to be unitarily similar if u au b for some unitary matrix u this expository paper surveys results on canonical forms and invariants for unitary similarity the first half gives a detailed description of methods developed by several authors brenner littlewood mitchell mcrae radjavi serge chuk and benedetti and cragnolini using inductively defined reduction procedures to transform matrices to canonical form the matrix is partitioned and successive unitary similarities applied to reduce the submatrices to some nice form at each stage one refines the partition and restricts the set of permissible unitary similarities to those that preserve the already reduced blocks the process ends in a finite number of steps producing both the canonical form and the subgroup of the unitary group that preserves that form depending on the initial step various canonical forms may be defined the method can also be used to define canonical forms relative to certain subgroups of the unitary group and canonical forms for finite sets of matrices under simultaneous unitary similarity the remainder of the paper surveys results on unitary invariants and other topics related to unitary similarity such as the specht pearcy trace invariants the numerical range and unitary reducibility

robust stability and stabilization of discrete singular systems an equivalent characterization this note deals with the problems of robust stability and stabilization for uncertain discrete time singular systems the parameter uncertainties are assumed to be time invariant and norm bounded appearing in both the state and input matrices a new necessary and sufficient condition for a discrete time singular system to be regular causal and stable is proposed in terms of a strict linear matrix inequality lmi based on this the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete time singular systems are introduced necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict lmi and a set of matrix inequalities respectively with these conditions the problems of robust stability and robust stabilization are solved an explicit expression of a desired state feedback controller is also given which involves no matrix decomposition finally an illustrative example is provided to demonstrate the applicability of the proposed approach