on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

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

abel lemma based finite sum inequality and its application to stability analysis for linear discrete time delay systems this paper is concerned with stability of linear discrete time delay systems note that a tighter estimation on a finite sum term appearing in the forward difference of some lyapunov functional leads to a less conservative delay dependent stability criterion by using abel lemma a novel finite sum inequality is established which can provide a tighter estimation than the ones in the literature for the finite sum term applying this abel lemma based finite sum inequality a stability criterion for linear discrete time delay systems is derived it is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a jensen type inequality approach and a free weighting matrix approach

brief paper a way to stabilize linear systems with delayed state a simple method is proposed for stabilizing linear systems with delayed state using linear feedback the method requires checking the negativity of a matrix containing two free parameters and solving a matrix lyapunov equation with these parameters a known stabilizability criterion and a simple stability theorem for the open loop system are obtained as special cases of the main result

integral points on abelian varieties the conjecture of lang referred to above asserts that the set in theorem 1 is finite for any choice of non constant function f such that f is ample it also applies to abelian varieties which are not jacobians using the standard trick of mapping an arbitrary abelian variety into a jacobian we can use theorem 1 to give other finiteness results 9 although not the strongest possible formulation we will content ourselves with the following which fits into the framework of the recent conjectures of vojta 9

robust stability and control of uncertain linear discrete time periodic systems with time delay this paper deals with the problems of robust stability analysis and robust control of linear discrete time periodic systems with a delayed state and subject to polytopic type parameter uncertainty in the state space matrices a robust stability criterion independent of the time delay length as well as a delay dependent criterion is proposed where the former applies to the case of a constant time delay and the latter allows for a time varying delay lying in a given interval the developed robust stability criteria are based on affinely uncertainty dependent lyapunov krasovskii functionals and are given in terms of linear matrix inequalities these stability conditions are then applied to solve the problems of robust stabilization and robust h control via static periodic state feedback numerical examples illustrate the potentials of the proposed robust stability and control methods

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

quadratic stabilizability of switched linear systems with polytopic uncertainties in this paper we consider quadratic stabilizability via state feedback for both continuous time and discrete time switched linear systems that are composed of polytopic uncertain subsystems by state feedback we mean that the switchings among subsystems are dependent on system states for continuous time switched linear systems we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices then the switched system is quadratically stabilizable via state feedback for discrete time switched linear systems we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non negative scalars and a common positive definite matrix for both continuous time and discrete time switched systems we propose the switching rules by using the obtained common positive definite matrix

generalized h2 control of switched discrete time systems with unknown delays the generalized h 2 control problem for a class of linear discrete time switched systems with constant unknown delays is investigated new linear matrix inequalities lmis characterization based on switched lyapunov krasovskii functional are established to guarantee the asymptotic stability and generalized h 2 performance design of generalized h 2 state feedback and dynamic output feedback controllers are developed a numerical example is worked out in detail to illustrate the theoretical developments

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

h sub infinity analysis and synthesis of discrete time systems with time varying uncertainty the problems of h sub infinity analysis and synthesis of discrete time systems with block diagonal real time varying uncertainty are considered it is shown that these problems can be converted into scaled h sub infinity analysis and synthesis problems the problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case the results on synthesis are established for general linear dynamic output feedback control

h sub spl infin state feedback control for discrete singular systems deals with the problem of state feedback h sub spl infin control for discrete singular systems it is not assumed that the singular system under consideration is necessarily regular the problem we address is the design of a state feedback controller such that the resulting closed loop system is not only regular causal and stable but also satisfies a prescribed h sub spl infin norm bound condition in terms of certain matrix inequalities a necessary and sufficient condition for the solution to this problem is obtained and a suitable state feedback control law is also given

the discrete time riccati equation related to the h sub spl infin control problem the h sub spl infin control problem has been solved recently with the use of discrete time algebraic riccati equations in this paper we investigate this riccati equation we derive recursive methods to find the stabilizing solution of this riccati equation moreover we derive several properties of the class of positive semi definite solutions of this equation

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

state feedback stabilization of nonlinear discrete time systems with time varying time delay abstract this paper deals with the class of nonlinear discrete time systems with varying time delay the problems of stability and stabilizability for this class of systems are considered given an upper bound and a lower bound on the time varying delay sufficient conditions for checking the stability of this class of systems are developed a control design algorithm is also provided for determining the state feedback controller gain all the results developed in this paper are in the lmi formalism which makes it easier to obtain them using existing tools a numerical example is provided to show the effectiveness of the results established

an algebraic approach to h output feedback control problems abstract we derive an output feedback controller which stabilizes a system and satisfies a prescribed h norm bound of the closed loop transfer function the proposed design method is available for any system i e there are no restrictions on d12 and d21 this approach utilizes only algebraic operations thus proofs are simple and clear

guaranteed cost control of uncertain discrete systems with delays in this paper we address the problems of robust performance analysis and control synthesis for a class of discrete time systems with parameter uncertainty and unknown state delay the parameter uncertainty is real time varying normbounded and the state delay is a constant within a prescribed interval for the robust performance analysis problem we adopt an appropriate notion of robust stability for discrete time uncertain time delay systems and show that this notion guarantees an upper bound on a linear quadratic cost function for the control synthesis problem we show that a robust state feedback controller can be constructed to render the closed loop system robustly stable while guaranteeing a prescribed level of performance the developed results are expressed in terms of algebraic matrix inequalities a numerical example is presented to illustrate the theory

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

new sufficient conditions for robust h fuzzy hyperbolic tangent control of uncertain nonlinear systems with time varying delay this paper considers the delay dependent robust h control problem based on fuzzy hyperbolic model fhm for a class of uncertain nonlinear systems with time varying delay firstly fhm modeling method is presented for uncertain nonlinear systems with time varying delay secondly the new delay dependent sufficient condition for the existence of a state feedback fuzzy hyperbolic tangent controller is proposed in terms of linear matrix inequalities lmis by constructing a novel lyapunov krasovskii functional the robust fhm based control law can guarantee that the closed loop system is robustly asymptotically stable with a prescribed h index as more information of the fhm and the size of time delay are taken into account the proposed conditions are new and less conservative finally three illustrative examples are given to show the effectiveness of using fhm based controllers

a lindemann weierstrass theorem for semi abelian varieties over function fields we prove an analogue of the lindemann weierstrass theorem that the exponentials of a q linearly independent set of algebraic numbers are algebraically independent replacing q alg by c t alg and g n by a semiabelian variety over c t alg both the formulations of our results and the methods are dierential algebraic in nature

output feedback control of switched nonlinear systems using multiple lyapunov functions abstract this work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints the key feature of the proposed methodology is the integrated synthesis via multiple lyapunov functions of lower level bounded nonlinear feedback controllers together with upper level switching laws that orchestrate the transitions between the constituent modes and their respective controllers both the state and output feedback control problems are addressed under the assumption of availability of full state measurements a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding stability region for each mode a set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed loop system when complete state measurements are unavailable a family of output feedback controllers are synthesized using a combination of bounded state feedback controllers high gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain a different set of switching rules based on the evolution of the state estimates generated by the observers is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes the differences between the state and output feedback switching strategies and their implications for the switching logic are discussed and a chemical process example is used to demonstrate the proposed approach

hybrid system stability and robustness verification using linear matrix inequalities this paper addresses issues concerning exponential stability and robustness of hybrid systems stability conditions using lyapunov techniques are given the search for the lyapunov functions is formulated as a linear matrix inequality lmi problem for hybrid systems with affine as well as non linear vector fields it is shown how the lyapunov approach most advantageously also can be used to guarantee stability despite the presence of model uncertainties several examples are given to illustrate the theory

model matching with strong stability in switched linear systems abstract this work deals with model matching by output dynamic feedback in switched linear systems the plant and the model are assumed to be subject to different switching signals a necessary and sufficient condition for achieving model matching with asymptotic stability of both the closed loop compensated system and the compensator for a sufficiently large dwell time is proven such condition is obtained by specializing the structural condition with a suitable redefinition of the robust controlled invariant subspace involved capable of capturing not only the structural aspect of the problem but also the stability aspects the effect of the combined action of nonzero initial states and nonzero inputs is dealt with the solution to a more demanding problem formulation where the dwell time is assumed to be fixed and given is also discussed

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

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

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

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

on function field mordell lang the semiabelian case and the socle theorem in this paper we complete our second generation model theoretic account of the function field mordell lang conjecture where we avoid appeal to dichotomy theorems for generalized zariski geometries in the current paper we reduce the semiabelian case to the abelian case using model theoretic tools we also use our results from 2 to prove modularity of the manin kernels over f p t sep in positive characterstic and over c t alg in characteristic 0

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

h control of discrete time linear systems with time varying delays in state this paper deals with the h control problems for discrete time linear systems with time varying delays in state in this paper the h control law is assumed to be a memoryless state feedback and the size of time varying delays considered is upper bounded the solution of the h control problem for discrete time linear systems with time varying delays in state can be obtained by solving an h control problem for auxiliary discrete time linear systems with no time delays

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

memoryless stabilization of linear delay differential systems sufficient conditions for memoryless feedback stabilization of linear time invariant delay differential systems are derived for both constant and time dependent delays

comments on bounded real criteria for linear time delay systems xiefu jiang et al point out some some misleading statements in the above mentioned paper shaked et al 1998 and relation results are given also wen shyong yu points out serious mistakes in the same paper and also untenable main results

output feedback h control of systems over communication networks using a deterministic switching system approach this paper proposes a new control problem of systems over asymmetric path delay configurations on arbitrary communication networks where the criterion is the h norm minimization via dynamic output feedback controllers network delay dependent switching controllers are designed via a piecewise lyapunov function approach as well as a common lyapunov function approach the controllers are found through convex optimization over linear matrix inequalities

the mordell lang conjecture for function fields we give a proof of the geometric mordell lang conjecture in any characteristic our method involves a model theoretic analysis of the kernel of manin s homomorphism and of a certain analog in characteristic p department of mathematics massachusetts institute of technology 2 277 cambridge massachusetts 02139 current address department of mathematics hebrew university jerusalem israel e mail address ehud math mit edu

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

groups definable in separably closed fields we consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection we prove in particular that no new definable groups arise in this way we show that any group definable in such a field l is definably isomorphic to the group of l rational points of an algebraic group defined over l

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

positive real control for 2 d discrete delayed systems via output feedback controllers this paper considers the problem of positive real control for two dimensional 2 d discrete delayed systems in the fornasini marchesini second local state space model attention is focused on the design of dynamic output feedback controllers which guarantee that the closed loop system is asymptotically stable and the closed loop transfer function is extended strictly positive real we first present a sufficient condition for extended strictly positive realness of 2 d discrete delayed systems based on this a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality lmi when the lmi is feasible an explicit parametrization of a desired output feedback controller is presented finally we provide a numerical example to demonstrate the application of the proposed method

integer points on curves of genus two and their jacobians let c be a curve of genus 2 defined over a number field and e the image of c embedded into its jacobian j we show that the heights of points of j which are integral with respect to 2 6 can be effectively bounded as a result if p is a point on c and p its image under the hyperelliptic involution then the heights of points on c which are integral with respect to p and p can be effectively bounded in such a way that we can isolate the dependence on p and show that if the height of p is bigger than some bound then there are no points which are s integral with respect to p and p we relate points on c which are integral with respect to p to points on j which are integral with respect to 6 and discuss approaches toward bounding the heights of the latter

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

memoryless h controllers for discrete time systems with time delay this paper considers the problem of h stabilization of discrete time systems with state delays and exogenous bounded energy l 2 disturbances specifically an h state feedback control design problem for discrete time systems with time delay is addressed the principal result involves sufficient conditions in terms of a modified riccati equation for characterizing state feedback controllers that enforce a bound on h performance and guarantee closed loop stability in the face of system state delay

delay dependent robust h control for uncertain discrete time singular systems with time delays the robust memoryless state feedback h control problem for uncertain time delay discrete time singular systems is discussed under a series of equivalent transformation the equivalence of this problem and the robust state feedback h control problem for standard state space uncertain time delay discrete time systems is presented in terms of matrix inequality the delay dependent sufficient condition for the solution of this problem is given the design method of the memoryless state feedback controller and the controller are also given

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

robust h control for uncertain discrete time systems with time varying delays via exponential output feedback controllers this paper considers the problem of robust h control for uncertain discrete systems with time varying delays the system under consideration is subject to time varying norm bounded parameter uncertainties in both the state and measured output matrices attention is focused on the design of a full order exponential stable dynamic output feedback controller which guarantees the exponential stability of the closed loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties in terms of a linear matrix inequality lmi a sufficient condition for the solvability of this problem is presented which is dependent on the size of the delay when this lmi is feasible the explicit expression of the desired output feedback controller is also given finally an example is provided to demonstrate the effectiveness of the proposed approach

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

h model reduction for discrete time delay systems delay independent and dependent approaches this paper investigates the problem of h model reduction for linear discrete time state delay systems for a given stable system our attention is focused on the construction of reduced order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed h error performance both delay independent and dependent approaches are developed with sufficient conditions obtained for the existence of admissible reduced order solutions since these obtained conditions are not expressed as strict linear matrix inequalities lmis the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved in standard numerical software in addition the development of reduced order models with special structures such as delay free models and zeroth order models is also addressed the approximation methods presented in this paper can be further extended to cope with systems with unc

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

h sub spl infin and positive real control for linear neutral delay systems this note is concerned with the h sub spl infin and positive real control problems for linear neutral delay systems the purpose of h sub spl infin control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the h sub spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level while the purpose of positive real control is to design a memoryless state feedback controller such that the resulting closed loop system is stable and the closed loop transfer function is extended strictly positive real sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality lmi when this lmi is feasible the expected memoryless state feedback controllers can be easily constructed via convex optimization

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

generalized h2 output feedback controller design for uncertain discrete time switched systems via switched lyapunov functions abstract this paper investigates the generalized h 2 control problem for a class of discrete time switched systems with uncertainties the uncertain system is modelled as a polytopic type with linear fractional uncertainty in the vertices by using switched lyapunov functions new linear matrix inequalities lmis characterizing the generalized h 2 performance for discrete time switched systems are obtained based on the result a generalized h 2 output feedback controller is developed for uncertain discrete time switched systems a numerical example is included to demonstrate the effectiveness of the proposed result

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

robust h control for uncertain discrete time systems with circular pole constraints this paper investigates the problem of robust h control for uncertain discrete time systems with circular pole constraints the system under consideration is subject to norm bounded time invariant uncertainties in both the state and input matrices the problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region and the h norm of the closed loop transfer function is strictly less than a given positive scalar for all admissible uncertainties by introducing the notion of quadratic d stabilizability with an h norm bound the problem is solved necessary and sufficient conditions for quadratic d stabilizability with an h norm bound are derived our results can be regarded as extensions of existing results on robust h control and robust pole assignment of uncertain systems

switched discrete time systems with time varying delays a generalized h2 approach in this paper we investigate the delay dependent performance analysis and control synthesis of a class of linear discrete time hybrid systems with time varying delays we employ hybrid lyapunov krasovskii functionals to establish the desired results under arbitrary switching a generalized h 2 approach is adopted and new parameterized linear matrix inequalities lmis characterization are developed to guarantee the delay dependent asymptotic stability design of generalized h 2 state feedback and dynamic output feedback controllers are subsequently constructed a numerical example is solved in detail to illustrate the theoretical developments

two riccati formulae for the discrete time h control problem a two riccati state space approach to the discrete time h control problem is presented the main theoretical tool is the kalman szego popov yakubovich system written in adequate forms in order to reduce the problems to a standard form for which the solutions are easily obtained the necessity part of our main results uses a signed counterpart of the positivity theorem

design of stabilizing switching control laws for discrete and continuous time linear systems using piecewise linear lyapunov functions in this paper the stability of switched linear systems is investigated using piecewise linear lyapunov functions in particular we identify classes of switching sequences that result in stable trajectories given a switched linear system we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system in the proposed approach we assume that each individual subsystem is stable and admits a piecewise linear lyapunov function based on these lyapunov functions we compose global lyapunov functions that guarantee stability of the switched linear system a large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space the approach is applied to both discrete time and continuous time switched linear systems

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

h sub infinity optimal one step ahead output feedback control of discrete time systems the discrete time one step ahead standard four blocks h sub infinity optimal control problem is considered the output feedback problem is transformed into a one step ahead h sub infinity optimal state estimation problem and the existing solution is used to derive the controller it is assumed that only previous measurements are available for control two results are obtained the first requires the solutions of two coupled riccati equations where the necessary and sufficient condition for the existence of the h sub infinity optimal result requires only the positive semidefiniteness of these solutions the second result applies two decoupled riccati equations with a coupling constraint as in the continuous time case and two additional conditions the derivation procedure is most simple and may thus provide considerable insight into the solution of the discrete time standard problem a similar procedure can also be used to obtain a solution to problems where the current measurement is available

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

quadratic stabilisation with h norm bound of non linear discrete time uncertain systems with bounded control the paper addresses the problem of quadratic stabilisability with h norm bound of uncertain discrete time control affine systems by norm bounded controls both structured parameter uncertainties and unstructured exogenous disturbances are taken into account the given definition of quadratic stabilisability is a generalisation of that used for linear systems so far a necessary condition of the stabilisability is formulated a state feedback control satisfying an a priori constraint is proposed for the solution of the formulated h problem the proposed method may be applicable even in such cases when the linearisation technique cannot be used

robust stability and performance via fixed order dynamic compensation the discrete time case a discrete time feedback control design problem involving parametric uncertainty is considered a quadratic bound suggested by recent work on discrete time state space h sub infinity theory is utilized in conjunction with the guaranteed cost approach to guarantee robust stability with a robust performance bound the principal result involves sufficient conditions for characterizing robust full and reduced order controllers with a worst case h sub 1 performance bound

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