an lmi approach to reliable guaranteed cost control of discrete time systems with actuator failure this paper is concerned with the reliable guaranteed cost control problem for discrete time systems with actuator failures and a given quadratic cost function the problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failure such that the cost function of the closed loop system is guaranteed to be no more than a certain upper bound a sufficient condition for the existence of reliable guaranteed cost controllers is derived via the linear matrix inequality lmi approach and a design procedure of such controllers is presented furthermore a convex optimization problem with lmi constraints is formulated to design the optimal reliable guaranteed cost controller which minimizes the upper bound of the closed loop system cost

robust stabilization of discrete time linear systems with norm bounded time varying uncertainty abstract this paper presents an algorithm for the stabilization of a class of discrete time uncertain systems suffering from uncertainty of the norm bounded time varying type the stabilizing control gain matrix is obtained by solving a certain discrete riccati equation the solution of this riccati equation is also a lyapunov matrix which is used to establish the stability of closed loop system the results presented in this paper generalize those obtained in previous works for continuous time uncertain systems

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

on extension of isometries between unit spheres of l γ type space and a banach space e abstract in this paper we study the isometric extension problem between the unit spheres of l type space and a banach space e we prove that every surjective isometry between the unit spheres s l and s e can be extended to be a linear isometry of l onto e moreover we study this problem between c and a banach space and also get an affirmative answer

a class of asymmetric simplicial finite element methods for solving finite incompressible elasticity problems abstract we consider the numerical solution of finite incompressible elasticity problems for mooney rivlin materials in n dimensional space n 2 3 in representing the displacement vector field with standard lagrange finite elements in general one faces the difficulty of the total number of constraints exceeding the total number of displacement degrees of freedom in the discrete problem if the nonlinear incompressibility condition is to be approximated within satisfactory accuracy in this paper we introduce a new class of piecewise reduced quadratic conforming simplicial finite elements that eliminates the above inconvenience with almost no extra implementational cost thereby allowing highly satisfactory approximate solutions this statement is illustrated by numerical examples in which our method is combined with an algorithm of augmented lagrangian type proposed by glowinski and le tallec for the continuous problem

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

correction to a stabilization algorithm for a class of uncertain linear systems abstract this note corrects an error in a recent paper on a stabilization algorithm for a class of uncertain linear systems the result of the paper was correct however the proof contained an error

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

robust h control for linear discrete time systems with norm bounded time varying uncertainty the problem of robust h analysis and synthesis for linear discrete time systems with norm bounded time varying uncertainty is studied in this paper it will be shown that this problem is equivalent to the problem of h analysis and synthesis of an auxiliary system the necessary and sufficient conditions for the equivalency are proved thus the original problem can be solved by existing h control methods

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

modelling and robust stability of networked control systems with packet reordering and long delay in this article modelling and robust stability of networked control systems ncs are discussed considering the existence of packet reordering and network induced delay a new mathematical model of ncs whose network induced delay is longer than one sampling period is obtained which can fully describe packet reordering and effectively eliminate the impact of packet reordering on the performance of ncs such that the newest control input can be executed by the actuator based on this model the time varying ncs is converted into an uncertain discrete linear system with multi step delay in terms of matrix theory furthermore a sufficient condition for robust stability of ncs is presented linear matrix inequality approach has been employed to solve the controller design problems numerical examples are compared with previous schemes to demonstrate the effectiveness of the proposed method

robust h sub 2 h sub spl infin filtering for linear systems with error variance constraints in this correspondence we consider the robust h sub 2 h sub spl infin filtering problem for linear perturbed systems with steady state error variance constraints the purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied 1 the filtering process is asymptotically stable 2 the steady state variance of the estimation error of each state is not more than the individual prespecified value 3 the transfer function from exogenous noise inputs to error state outputs meets the prespecified h sub spl infin norm upper bound constraint we show that in both continuous and discrete time cases the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like equations inequalities we present both the existence conditions and the explicit expression of desired robust filters an illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach

technical communique stability and stabilization of nonuniform sampling systems this paper is concerned with nonuniform sampling systems where the sampling interval is time varying within a certain known bound the system is transformed into a time varying discrete time system where time varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques to reduce conservatism arising from modeling time varying parts as a single uncertainty the time varying parts are modeled as n uncertainties with larger n a less conservative stability condition is derived at sacrifice of more computation it is shown through a numerical example that the proposed stability condition is better than existing stability conditions

isometries on unit sphere of lβn in this paper we characterize isometries between unit spheres of f space furthermore we study the isometric extension problem on such kind of metric linear spaces

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

stability positive invariance and design of constrained regulators for networked control systems in this article the stability analysis the positive invariance of polyhedral sets and the design of state feedback regulators for networked control systems ncs with bounded transmission delays constant and unknown or time varying are investigated the dynamics of the ncs is described by autoregressive moving average arma models contrary to former approaches based on quadratic lyapunov functions in this article polyhedral lyapunov functions are used for both stability and positive invariance analysis and state feedback synthesis then based on the property that the exponential of a matrix can be expressed as a weighted sum of its constituent matrices it is proven that the problems of determination of stability margins or the design of stabilising controllers can be reduced to linear programming optimisation problems the use of arma models allows the development of methods for the design of state feedback controllers satisfying state constraints or convergence rate specifications defined on the

characterizations on mazur ulam theorem abstract we consider the area preserving 2 isometries in linear 2 normed spaces in chu 2007 10 the mazur ulam theorem was proved in linear 2 normed spaces with the assumption of the collinearity preserving in this article we prove the mazur ulam theorem for the interior preserving mappings in linear 2 normed spaces recently amyari sadeghi 16 in non archimedean 2 normed spaces the mazur ulam theorem was proved under the condition of strict convexity in this paper we also prove the theorem on non archimedean 2 normed spaces over a linear ordered non archimedean field without the strict convexity assumption

properties of isometric mappings abstract some relations between isometry and linearity are examined in particular generalizations of the mazur ulam theorem and open problems are discussed

characterizations on isometries in linear n normed spaces abstract let f x y be a weak n isometry in linear n normed spaces in this paper we prove that if f satisfies some conditions then f is an n isometry

the aleksandrov problem in linear 2 normed spaces we introduce the concept of 2 isometry which is suitable to represent the notion of area preserving mappings in linear 2 normed spaces and then we obtain some results for the aleksandrov problem in linear 2 normed spaces

the problem of isometric extension in the unit sphere of the space sp α abstract in this paper we present an isometric extension from the unit sphere of a subspace of s p to the whole space s p we obtain that the lamperti isometric mapping of the unit sphere s s p into itself can be extended to an isometry on the whole space s p

brief paper analysis of networked control systems with drops and variable delays motivated by the insertion of a communication network in the feedback control loop this paper focuses on how network induced data dropouts and variable delays affect the stability of a linear plant with state feedback control sufficient conditions for lyapunov stability are derived in the case of uncertainty due to drops and delays the verification problem of the sufficient conditions can be directly cast as an lmi feasibility problem we illustrate the methodology by an example in the cases of drops delays and drops with delays

a dynamic output feedback controller for ncs based on delay estimates the stabilization of a network controlled system including a global time varying delay is investigated in this note this delay is considered to be unknown but it is assumed that a bounded error estimate is available the exponential uncertainty induced by the time varying delay is decomposed into the sum of a polytopic term and an uncertain bounded term sufficient conditions to design a dynamic output feedback controller depending on an estimate of the time varying delay are proposed as linear matrix inequalities an illustration shows how our methodology enlarges the design techniques of the literature

inequalities for distances between points and distance preserving mappings abstract in this paper we generalize the short diagonals lemma by proving a new inequality for distances between six points moreover we apply this inequality to a partial solution to the aleksandrov rassias problem

brief paper input to state stability for networked control systems via an improved impulsive system approach this paper presents a novel impulsive system approach to input to state stability iss analysis of networked control systems ncss with time varying sampling intervals and delays this approach is based upon the new idea that an ncs can be viewed as an interconnected hybrid system composed of an impulsive subsystem and an input delay subsystem a new type of time varying discontinuous lyapunov krasovskii functional which makes full use of the information on the piecewise constant input and the bounds of the network delays is introduced to analyze the iss property of ncss linear matrix inequality based sufficient conditions are derived for iss of ncss with respect to external disturbances when applied to the approximate tracking problem for ncss the derived iss result provides bounds on the steady state tracking error numerical examples are provided to show the efficiency of the proposed approach

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

robust stabilization for a class of discrete time non linear systems via output feedback the unified lmi approach this paper discusses a robust stabilization problem for a class of multi input and multi output mimo discrete time non linear systems with both state and control inputs containing non linear perturbations the problem is solved via static output feedback and dynamic output feedback respectively a unified approach is used to cast the problem into a convex optimization involving linear matrix inequalities lmi all the controllers can robustly stabilize the systems and maximize the bound on the non linear perturbations this paper also extends the output feedback centralized design approach to a class of discrete time mimo non linear decentralized systems both robust static and dynamic output feedback controllers are obtained

non fragile exponential stability assignment of discrete time linear systems with missing data in actuators this technical note is concerned with the non fragile exponential stabilization for a class of discrete time linear systems with missing data in actuators the process of missing data is modeled by a discrete time markov chain with two state components when no uncertainty exists in the controllers a necessary and sufficient condition which not only guarantees the exponential stability but also gives a lower bound on the decay rate is established in terms of linear matrix inequalities lmis based on this condition an lmi based approach is provided to design a non fragile state feedback controller such that the closed loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers a numerical example is provided to show the effectiveness of the theoretical results

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

h sub spl infin output feedback control of discrete time fuzzy systems with application to chaos control this paper presents an observer based h sub spl infin output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise lyapunov function the basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities lmis that are numerically feasible with commercially available software application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method

on the generalizations of the mazur ulam isometric theorem abstract this paper contains several generalizations of the mazur ulam isometric theorem in f spaces which are not assumed to be locally bounded let x and y be two real f spaces and let x be locally pseudoconvex or midpoint bounded assume that a operator t maps x onto y in a locally 1 2i isometric manner for all i 0 n then t is affine in addition we give the sufficient conditions of a mapping between two topological vector spaces being affine

a contribution to the aleksandrov conservative distance problem in two dimensions abstract let e be a two dimensional real normed space in this paper we show that if the unit circle of e does not contain any line segment such that the distance between its endpoints is greater than 1 then every transformation e e which preserves the unit distance is automatically an affine isometry in particular this condition is satisfied when the norm is strictly convex

a fixed point theorem in n banach spaces and ulam stability abstract motivated by some issues in ulam stability we prove a fixed point theorem for operators acting on some classes of functions with values in n banach spaces we also present applications of it to ulam stability of eigenvectors and some functional and difference equations

an inequality for distances between 2n points and the aleksandrov rassias problem in this paper we introduce an inequality for distances between every two points among the given 2n points and apply this inequality to a partial solution of the aleksandrov rassias problem which was first posed by th m rassias

characterizations on 2 isometries we consider 2 isometries weak 2 isometries and 2 continuous mappings and investigate the relation between three mappings in linear 2 normed spaces also we prove that the riesz theorem holds when x is a linear 2 normed spaces

on the aleksandrov problem in linear n normed spaces the aim of this article is to generalize the aleksandrov problem to the case of linear n normed spaces

stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix this paper presents a procedure for stabilizing a class of uncertain linear systems the uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters this matrix of uncertain parameters may be time varying however it is constrained by a bound on its induced norm the stabilization procedure presented involves the repeated solution of an algebraic riccati equation when a positive definite solution to this riccati equation is obtained this solution is used to construct a stabilizing linear control law another important result contained in this paper can be stated roughly as follows for the class of uncertain systems under consideration if a system can be stabilized via nonlinear control then it is also possible to stabilize the system via linear control

a fixed point approach to the stability of isometries in this paper we apply a fixed point theorem to the proof of hyers ulam rassias stability property for isometries from a normed space into a banach space in which the parallelogram law holds

numerical solution of problems in incompressible finite elasticity by augmented lagrangian methods ii three dimensional problems in a first paper siam j appl math 42 1982 pp 400 429 we introduced an augmented lagrangian methodology for solving equilibrium problems in incompressible finite elasticity and then applied it to the solution of several two dimensional and axisymmetric test problems in this second paper we extend our methods to the solution of genuine three dimensional problems actually using these augmented lagrangian techniques we can reduce the solution of these complicated nonlinear nonconvex problems to the solution of a sequence of linear problems and also to the solution of a sequence of minimization problems for convex functionals on convex sets the capabilities of our methods are illustrated by the results of numerical experiments

isometries mazur ulam theorem and aleksandrov problem for non archimedean normed spaces abstract we study isometries between normed spaces over a non archimedean valued field k we show the failure of a mazur ulam theorem in the framework of non archimedean spaces considering aleksandrov problem we prove that a surjective lipschitz map e e with the strong distance one preserving property where e is a finite dimensional normed space is an isometry if and only if k is locally compact we prove also that every isometry e e for finite dimensional e is surjective if and only if k is spherically complete and card k is finite

the mazur ulam property for two dimensional somewhere flat spaces abstract in this paper we show that if x is a two dimensional real normed space such that its unit sphere contains a line segment with the distance between its endpoints being greater than 1 then x has the mazur ulam property that is every isometry from the unit sphere of x onto the unit sphere of any normed space y can be extended to a linear isometry from x onto y

h sub 2 guaranteed cost control for singularly perturbed uncertain systems the h sub 2 guaranteed cost control problem for a singularly perturbed norm bounded uncertain system is addressed using the quadratic stabilizability framework after defining the corresponding slow and fast uncertain subsystems the set of quadratic stabilizing composite controls is characterized two riccati equations have to be solved one for the slow subsystem and the other for the fast subsystem choosing appropriately the weighting matrices it is shown how to pick up in the set of quadratic stabilizing composite controls a control minimizing an upper bound on the h sub 2 norm of a certain transfer matrix the case of the guaranteed cost control problem for the reduced system is also investigated

guaranteed cost control for discrete time linear systems under controller gain perturbations abstract this paper considers the problem of guaranteed cost control for discrete time linear systems under state feedback control gain perturbations two classes of perturbations are considered namely additive and multiplicative the state feedback control designs for optimal guaranteed cost control under the two classes of gain perturbations are given in terms of solutions to algebraic riccati equations the designs are such that the cost of the closed loop system is guaranteed to be within a certain bound for all admissible uncertainties numerical examples are included to illustrate the design procedures

brief robust stabilization and guaranteed cost control for discrete time linear systems by static output feedback this paper proposes a systematic approach for the static output feedback control design for discrete time uncertain linear systems it is shown that if the open loop system satisfies some particular structural conditions and the uncertainty has a specific structure a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the strongest one relies on a minimum phase argument square and nonsquare systems are considered the performance problem through a quadratic criterion is also discussed guaranteed cost control

mappings of conservative distances and the mazur ulam theorem abstract let x and y be two real hilbert spaces with the dimension of x greater than 1 several cases about the aleksandrov rassias problem for t x y preserving two or three distances are presented and geometric interpretations of these cases are also given

mappings of conservative distances in linear n normed spaces abstract the aim of this article is to generalize the mazur ulam theorem to the case of linear n normed spaces

equimodular and linearity in modular spaces abstract in this paper the concept of equimodular is introduced it contains several generalizations of mazur ulam s isometric theorem in modular spaces let x and y be two real modular spaces and x with 1 midpoint shrinking whose modular x satisfies the 2 condition assume that an operator t maps x onto y in an 2 ti equimodular manner for all i 0 n where ti is a null sequence of nonnegative reals with the property that t0 1 t1 1 2 and ti ti 1 2ti for i 2 then t is affine

robust decentralized stabilization of a class of linear discrete time systems with non linear interactions this paper deals with robust stabilization of a class of linear discrete time systems under non linear perturbations via output feedback a bound on the non linear perturbations is maximized in the design it is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non linear perturbations an improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem consequently the proposed method can yield a much less conservative result than that of earlier methods of major interest is an extension to a class of interconnected systems composed of linear subsystems with non linear interactions a robust decentralized controller is presented such that the closed loop systems are maximally tolerant to interconnected non linear couplings numerical examples i

robust stability bounds on time varying perturbations for state space models of linear discrete time systems the stability robustness of linear discrete time systems in the time domain is addressed using the lyapunov approach bounds on linear time varying perturbations that maintain the stability of an asymptotically stable linear time invariant discrete time nominal system are obtained for both structured and unstructured independent perturbations bounds are also derived assuming that various elements of the system matrix are perturbed dependently the result for the structured perturbation case is extended to the stability analysis of interval matrices

stability analysis of networked control systems a sum of squares approach this paper presents a sum of squares sos approach to the stability analysis of networked control systems ncss incorporating bounded time varying delays bounded time varying transmission intervals and a shared communication medium a shared communication medium imposes that per transmission only one node which consists of several actuators or sensors can access the network and transmit its corresponding data which node obtains access is determined by a network protocol we will provide mathematical models that describe these ncss and transform them into suitable hybrid systems formulations based on these hybrid systems formulations we construct lyapunov functions using sos techniques that can be solved using lmi based computations this leads to several beneficial features i we can deal with plants and controllers which are described by nonlinear piecewise polynomial differential equations ii we can allow for non zero lower bounds on the delays and transmission intervals in contrast with various existing approaches iii we allow more flexibility in the lyapunov functions thereby obtaining less conservative estimates of the maximal allowable transmission intervals mati and maximal allowable delay mad and finally iv it provides an automated method to address stability analysis problems in ncs several numerical examples illustrate the strengths of our approach

optimal guaranteed cost control of uncertain discrete time delay systems this paper considers the problem of robust guaranteed cost control of linear discrete time delay systems with parametric uncertainties by matrix inequality approach the robust quadratic stability of the system is studied a control design method is developed such that the closed loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays furthermore the upper bound cost can be optimized by incorporating with a minimization problem a numerical example is given to show the potential of the proposed techniques

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

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

on extension of isometries and approximate isometries between unit spheres article history received 10 april 2008 available online 19 november 2008 submitted by j bastero

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

on the positive invariance of polyhedral sets for discrete time systems abstract in this note necessary and sufficient conditions for a polyhedral set to be a positively invariant set of a linear discrete time system are established

comparison principle positive invariance and constrained regulation of nonlinear systems abstract in this paper the comparison principle is applied to the design of feedback controllers for nonlinear discrete time systems subject to physical constraints first the connection between the comparison principle and the existence of positively invariant sets of a special form is established and polyhedral positively invariant sets for nonlinear systems are obtained then these results are applied to the determination of state feedback control laws that transfer to the origin all initial states of a prespecified region of the state space without violation of physical constraints on the control vector

asymptotic properties of isometries abstract in this paper we prove two theorems on the local stability of isometries in connection with e p isometries these theorems reveal that a large class of e p isometries defined on various restricted domains are stable

stability of networked control systems with polytopic uncertainty and buffer constraint we consider the stability of the discrete time networked control systems ncss with polytopic uncertainty where a smart controller is updated with the buffered sensor information at stochastic intervals and the amount of the buffered data received by the controller under the buffer capacity constraint is also random we establish sufficient conditions for guaranteeing the exponential stability of generic switched ncss and the exponential mean square stability of markov chain driven ncss respectively an illustrative example is given to demonstrate the effectiveness of our results

controller synthesis for networked control systems this paper presents a discrete time model for networked control systems ncss that incorporates all network phenomena time varying sampling intervals packet dropouts and time varying delays that may be both smaller and larger than the sampling interval based on this model constructive lmi conditions for controller synthesis are derived such that stabilizing state feedback controllers can be designed besides the proposed controller synthesis conditions a comparison is made between the use of parameter dependent lyapunov functions and lyapunov krasovskii functions for stability analysis several examples illustrate the effectiveness of the developed theory

stabilization of uncertain discrete time linear system with limited communication this technical note proposes a procedure to control an uncertain discrete time networked system using an aperiodic stabilizing input information the system is primarily affected by the time varying norm bounded mismatched parametric uncertainty aperiodic exchange of information is done due to bandwidth constraint of the communication network an event triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks in event triggered control the control input is computed and actuated at the system end only when a pre specified event condition is violated the robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost functional it is shown that the robust control law with aperiodic information ensures input to state stability iss of the original system in the presence of mismatched uncertainty deriving the event triggering condition for a discrete time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note a numerical example is given to prove the efficacy of the proposed event based control algorithm over the conventional periodic one

on the mazur ulam problem in linear 2 normed spaces abstract we study the notion of 2 isometry which is suitable to represent the concept of area preserving mapping in linear 2 normed spaces and then prove the mazur ulam problem in linear 2 normed spaces

isomorphisms between unital c algebras abstract it is shown that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all unitaries u a all y a and n 0 1 2 and that almost linear continuous bijection h a b of a unital c algebra a of real rank zero onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all u v a v v v 1 v is invertible all y a and n 0 1 2 assume that x and y are left normed modules over a unital c algebra a it is shown that every surjective isometry t x y satisfying t 0 0 and t u x u t x for all x x and all unitaries u a is an a linear isomorphism this is applied to investigate c algebra isomorphisms between unital c algebras

une methode numerique pour les problemes d equilibre de corps hyperelastiques compressibles en grandes deformations cet article applique les techniques de lagrangien augmente a la resolution numerique des problemes d equilibre de corps hyperelastiques compressibles soumis a de grandes deformations la methode obtenue est illustree par plusieurs exemples numeriques this paper uses augmented lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations the resulting method is illustrated by several numerical examples

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

robust stability analysis of networked systems with varying delays this article is concerned with networked controlled systems ncs with uncertain varying bounded transmission delays and asynchronous discrete time static control laws it is first shown that the delay variation gives rise to a discrete time uncertain ncs model robust stability analysis is carried out via a linear matrix inequality approach which when combined with a directed parameter search yields an estimate of robust stability bounds against any variations of the maximum allowable delay constrained within one sampling period that the closed loop system can tolerate the derived bounds are compared with other techniques relying on the singular values of the perturbed ncs model the presented simulation results prove the efficacy of the proposed control scheme

robust stability bounds for multi delay networked control systems abstractin this paper the robust stability of a perturbed linear continuous time system is examined when controlled using a sampled data networked control system ncs framework three new robust stability bounds on the time invariant perturbations to the original continuous time plant matrix are presented guaranteeing stability for the corresponding discrete closed loop augmented delay free system adfs with multiple time varying sensor and actuator delays the bounds are differentiated from previous work by accounting for the sampled data nature of the ncs and for separate communication delays for each sensor and actuator not a single delay therefore this paper expands the knowledge base in multiple inputs multiple outputs mimo sampled data time delay systems bounds are presented for unstructured semi structured and structured perturbations

technical communique robust h control of discrete systems with uncertain parameters and unknown delays in this paper we address the problems of robust h performance analysis and control synthesis for a class of discrete time systems with norm bounded parameter uncertainty and unknown constant state delay through finite dimensional algebraic riccati equations we provide a necessary and sufficient condition for designing a memoryless state feedback controller which stabilizes the discrete time delay system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays an example is worked out to illustrate the developed theory