necessary conditions of asymptotic stability for unilateral dynamical systems in this paper we develop a mathematical tool that can be used to state necessary conditions of asymptotic stability of isolated stationary solutions of a class of unilateral dynamical systems more precisely nonlinear evolution variational inequalities are considered instability criteria are also given applications can be found in mechanics or electrical circuits

h tracking of uncertain stochastic time delay systems the problem of state robust h tracking control for uncertain stochastic systems with interval time varying delay is considered in this paper the target is to design a memory state feedback controller such that the resulting closed loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given h performance firstly by constructing delay partitioning dependent lyapunov krasovskii functional with reciprocally convex approach a delay dependent condition guaranteeing the robust h tracking performance is proposed in a set of matrix inequalities secondly new stability criteria for stochastic systems with time varying delay are given with less conservativeness than some recent results thirdly memory state feedback controller is designed via a set of linear matrix inequalities lmis which can be solved by matlab lmi toolbox at last numerical simulations are addressed to show the effectiveness of the proposed methods

differential variational inequalities this paper introduces and studies the class of differential variational inequalities dvis in a finite dimensional euclidean space the dvi provides a powerful modeling paradigm for many applied problems in which dynamics inequalities and discontinuities are present examples of such problems include constrained time dependent physical systems with unilateral constraints differential nash games and hybrid engineering systems with variable structures the dvi unifies several mathematical problem classes that include ordinary differential equations odes with smooth and discontinuous right hand sides differential algebraic equations daes dynamic complementarity systems and evolutionary variational inequalities conditions are presented under which the dvi can be converted either locally or globally to an equivalent ode with a lipschitz continuous right hand function for dvis that cannot be so converted we consider their numerical resolution via an euler time stepping procedure which involves the solution of a sequence of finite dimensional variational inequalities borrowing results from differential inclusions dis with upper semicontinuous closed and convex valued multifunctions we establish the convergence of such a procedure for solving initial value dvis we also present a class of dvis for which the theory of dis is not directly applicable and yet similar convergence can be established finally we extend the method to a boundary value dvi and provide conditions for the convergence of the method the results in this paper pertain exclusively to systems with index not exceeding two and which have absolutely continuous solutions

neighborhood systems for production sets with indivisibilities a production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values a neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors the neighborhood relation is assumed to be symmetric and translation invariant each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities it is shown that each technology matrix subject to mild regularity assumptions has a unique minimal neighborhood system for which a local maximum is global the complexity of such minimal neighborhood systems is examined for several examples

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

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

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

the topological structure of maximal lattice free convex bodies the general case given a genericm n matrixa the simplicial complexk a is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form x ax b the main result of this paper is that the topological space associated withk a is homeomorphic withrm 1 1998 the mathematical programming society inc published by elsevier science b v

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

on a new class of differential variational inequalities and a stability result this paper addresses a new class of differential variational inequalities that have recently been introduced and investigated in finite dimensions as a new modeling paradigm of variational analysis to treat many applied problems in engineering operations research and physical sciences this new subclass of general differential inclusions unifies ordinary differential equations with possibly discontinuous right hand sides differential algebraic systems with constraints dynamic complementarity systems and evolutionary variational systems the purpose of this paper is two fold firstly we show that these differential variational inequalities when considering slow solutions and the more general level of a hilbert space contain projected dynamical systems another recent subclass of general differential inclusions this relation follows from a precise geometric description of the directional derivative of the metric projection in hilbert space which is based on the notion of the quasi relative interior secondly we are concerned with stability of the solution set to this class of differential variational inequalities here we present a novel upper set convergence result with respect to perturbations in the data including perturbations of the associated set valued maps and the constraint set here we impose weak convergence assumptions on the perturbed set valued maps use the monotonicity method of browder and minty and employ mosco convergence as set convergence also as a consequence we obtain a stability result for linear complementarity systems

sliding mode variable structure control for parameter uncertain stochastic systems with time varying delay in this paper the variable structure control problem for a class uncertain of stochastic system with time varying delay is investigated firstly a new concept of the subordinated reachability of the sliding motion is introduced to approach approximately the specified sliding surface the variable structure control law is then proposed to ensure that the sliding motion is subordinated reachable furthermore a sufficient condition for mean square asymptotical stability of the sliding motion is given finally a numerical example is presented to demonstrate the effectiveness of the obtained results

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

stability and instability matrices for linear evolution variational inequalities this paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems represented as linear evolution variational inequalities levi such systems can also be seen as a sort of differential inclusion or in special cases as linear complementarity systems which in turn are a class of hybrid dynamical systems examples show that the stability of the unconstrained system and that of the constrained system may drastically differ various criteria are proposed to characterize the stability or the instability of levi

absolute stability and the lagrange dirichlet theorem with monotone multivalued mappings abstract this note presents an extension of the absolute stability problem and of the lagrange dirichlet theorem when the nonlinearities entering the model are considered within the class of monotone multivalued mappings consequently including operators with piecewise linear graphs that may represent physical effects like coulomb friction dead zones saturations elasto plasticity and unilateral constraints

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

positive solutions of variational inequalities a degree theoretic approach if the mapping a is strictly monotone and coercive is equivalent to a fixed point equation u m u in k cf section 1 suppose that m is continuous and maps bounded subsets of k into compact ones then due to the fact that k is a retract of x it is possible to define a fixed point index of m with properties similar to those associated with the leray schauder degree 1 sect 111 in section 1 we introduce another index which is based on the previous one but has the advantage of being directly related to inequality rather than to the fixed point equation u m u in section 2 we apply this new index in order to show that if c is a closed convex subset of k then under suitable assumptions upon f the set of solutions of the inequality

some results on the controllability of planar variational inequalities abstract this note deals with the controllability of a class of planar complementarity dynamical systems which can also be viewed as planar evolution variational inequalities it is shown that the complementarity conditions influence the controllability of the system a lot

cellular resolutions of monomial modules we construct a canonical free resolution for arbitrary monomial modules and lattice ideals this includes monomial ideals and defining ideals of toric varieties and it generalizes our joint results with irena peeva for generic ideals bps ps introduction given a field k we consider the laurent polynomial ring t k x 1 1 x 1 n as a module over the polynomial ring s k x1 xn the module structure comes from the natural inclusion of semigroup algebras s k n k z t a monomial module is an s submodule of t which is generated by monomials x x1 1 xan n a z of special interest are the two cases when m has a minimal monomial generating set which is either finite or forms a group under multiplication in the first case m is isomorphic to a monomial ideal in s in the second case m coincides with the lattice module ml s x a l k x b n l t for some sublattice l z whose intersection with n is the origin 0 0 0 we shall derive free resolutions of m from regular cell complexes whose vertices are the generators of m and whose faces are labeled by the least common multiples of their vertices the basic theory of such cellular resolutions is developed in section 1 our main result is the construction of the hull resolution in section 2 we rescale the exponents of the monomials in m so that their convex hull in r is a polyhedron pt whose bounded faces support a free resolution of m this resolution is new and interesting even for monomial ideals it need not be minimal but unlike minimal resolutions it respects symmetry and is free from arbitrary choices in section 3 we relate the lattice module ml to the z l graded lattice ideal il x x a b l s this class of ideals includes ideals defining toric varieties we express the cyclic smodule s il as the quotient of the infinitely generated s module ml by the action of l in fact we like to think of ml as the universal cover of il many questions about il can thus be reduced to questions about ml in particular we obtain the hull resolution of a lattice ideal il by taking the hull resolution of ml modulo l this paper is inspired by the work of barany howe and scarf bhs who introduced the polyhedron pt in the context of integer programming the hull resolution generalizes results in bps for generic monomial ideals and in ps for generic lattice ideals in these generic cases the hull resolution is minimal

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

test sets for integer programs in this paper i discuss various properties of the simplicial complex of maximal lattice free bodies associated with a matrix a if the matrix satisfies some mild conditions and is generic the edges of the complex form the minimal test set for the family of integer programs obtained by selecting a particular row of a as the objective function and using the remaining rows to impose constraints on the integer variables 1997 the mathematical programming society inc published by elsevier science b v

technical communique on delay dependent stability and decay estimate for uncertain systems with time varying delay in this note for a class of linear uncertain systems with time varying delay a delay dependent robust stability criterion which can give information on the decay rate of the systems state is presented

the complex of maximal lattice free simplices the simplicial complex k a is defined to be the collection of simplices and their proper subsimplices representing maximal lattice free bodies of the form x ax b with a a fixed generic n 1 n matrix the topological space associated with k a is shown to be homeomorphic to n and the space obtained by identifying lattice translates of these simplices is homeorphic to the n torus

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 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

robust stability criterion for uncertain stochastic systems with time varying delay via sliding mode control abstract this paper is focused on sliding mode control smc for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and stochastic perturbations may appear in the controlled system a new integral type switching surface function is first constructed then a sufficient condition for the existence of sliding surface is established in terms of linear matrix inequalities lmis by employing some free weighting matrices which guarantees the robustly stochastically stable of the sliding mode dynamic system with time varying delay for all admissible uncertainties moreover a smc law is synthesized to drive the system state trajectories onto the predefined switching surface in a finite time finally a simulation example is provided to illustrate the effectiveness of the proposed theory

on exponential stabilization for a class of neutral type systems with parameter uncertainties an integral sliding mode approach this paper is focused on integral sliding mode control ismc for a class of parameter uncertain neutral type systems with time varying delays ntstd an integral sliding surface functional is firstly constructed for the ntstd then a delay dependent robust stability criterion is established for all admissible uncertainties which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate in addition by solving the generalized eigenvalue problem gevp presented in the subsequent work the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived furthermore a sliding mode control smc law is then synthesised to ensure the stability of the closed loop system and the proposed smc law can drive the state of controlled dynamic system into the predefined sliding surface in finite time finally a numerical example is provided to demonstrate the effectiveness of the obtained results

robust stabilization of uncertain systems with time varying multistate delay the authors deal with the problem of stabilizing a class of uncertain linear systems with time varying multi state delay and subject to norm bounded parameter uncertainty via memoryless linear state feedback some sufficient conditions for the robust stabilizability are derived fur this class of uncertain systems if there exists a positive definite symmetric solution satisfying the algebraic riccati equation or inequality a suitable memoryless state feedback law can be derived also moreover all such parametric algebraic riccati inequalities have been transformed into some linear matrix inequality problems so there is no tuning of the parameters to gain a stabilizing solution

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

on the principle of linearized stability for variational inequalities on etudie la stabilite des solutions stationnaires d inegalites variationnelles paraboliques dans des espaces de hilbert

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

delay dependent robust stability and stabilization of uncertain linear delay systems a linear matrix inequality approach this paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time delay the uncertainty is assumed to be norm bounded and appears in all the matrices of the state space model we develop methods for robust stability analysis and robust stabilization the proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities

on two parameter global bifurcation of periodic solutions to a class of differential variational inequalities abstract in this paper by using the method of integral guiding functions a multiparameter global bifurcation theorem for differential inclusions with the periodic condition is proved it is shown how the abstract result can be applied to the study of the two parameter global bifurcation of periodic solutions for a class of differential variational inequalities

nonlocal problem for differential complementarity systems in this paper by using the topological degree theory for multivalued maps and the bounding function method we give sufficient conditions for the existence of solutions to a nonlocal problem of differential complementarity systems an example is given

integral polyhedra in three space in a series of recent papers i have introduced a particular class of convex polyhedra in rn arising in the study of integer programming problems with n variables in the present paper a detailed analysis of these polyhedra will be given for the case in which n 3 the analysis is based on an unpublished theorem demonstrated several years ago by roger howe which seems to have no immediate generalization to higher values of n

brief paper smc design for robust h control of uncertain stochastic delay systems recently sliding mode control method has been extended to accommodate stochastic systems however the existing results employ an assumption that may be too restrictive for many stochastic systems this paper aims to remove this assumption and present in terms of lmis a sliding mode control design method for stochastic systems with state delay in some cases the proposed method provides a control scheme for finite time stabilization of stochastic delay systems

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

lyapunov stability of complementarity and extended systems a linear complementarity system lcs is a piecewise linear dynamical system consisting of a linear time invariant ordinary differential equation ode parameterized by an algebraic variable that is required to be a solution to a finite dimensional linear complementarity problem lcp whose constant vector is a linear function of the differential variable continuing the authors recent investigation of the lcs from the combined point of view of system theory and mathematical programming this paper addresses the important system theoretic properties of exponential and asymptotic stability for an lcs with a c 1 state trajectory the novelty of our approach lies in our employment of a quadratic lyapunov function that involves the auxiliary algebraic variable of the lcs when expressed in the state variable alone the lyapunov function is piecewise quadratic and thus nonsmooth the nonsmoothness feature invalidates standard stability analysis that is based on smooth lyapunov functions in addition to providing sufficient conditions for exponential stability we establish a generalization of the well known lasalle invariance theorem for the asymptotic stability of a smooth dynamical system to the lcs which is intrinsically a nonsmooth system sufficient matrix theoretic copositivity conditions are introduced to facilitate the verification of the stability properties properly specialized the latter conditions are satisfied by a passive like lcs and certain hybrid linear systems having common quadratic lyapunov functions we provide numerical examples to illustrate the stability results we also develop an extended local exponential stability theory for nonlinear complementarity systems and differential variational inequalities based on a new converse theorem for odes with b differentiable right hand sides the latter theorem asserts that the existence of a b differentiable lyapunov function is a necessary and sufficient condition for the exponential stability of an equilibrium of such a differential system

robust stabilization of uncertain time delay systems with fractional stochastic noise using the novel fractional stochastic sliding approach and its application to stream water quality regulation in this paper stochastic systems with fractional gaussian noise fgn are stochastically stabilized using a new robust sliding mode control scheme the system is assumed to have state time delay and the system matrices have uncertainties the proposed sliding hyper surface is a fractional ito process which is proven to be attainable almost surely in finite time by applying the fractional ito formula the trajectories of the system will be kept within a time varying region around the sliding hyper surface the stochastic asymptotic stability of the closed loop dynamics at sliding mode is guaranteed by the feasibility of some linear matrix inequalities lmis the usefulness of the theoretical findings is demonstrated by providing a case study on the problem of stream water quality standards regulation in addition to show the effectiveness and superiority of the method a numerical example is presented

the contact problem for linear continuous time dynamical systems a geometric approach in this paper linear time invariant dynamical systems described by a combination of differential equalities and static inequalities in state space formulation are investigated of special interest is the contact problem the effect of the boundary of the constraint set on the behavior of the system this effect is studied by dividing the state space in a number of disjunct subsets it is shown that these subsets are invariant under linear state feedback in our framework a specific place is reserved for modeling the laws of collision i e physical modeling which are regarded as external factors our main results are a system theoretical framework in which we describe what happens upon contact and a definition of the constrained state space system in terms of its restricted behavior the results presented here can be considered as an extension for restricted linear systems of the classic positive invariance theory for linear systems

robust control of delay systems a sliding mode control design via lmi this paper considers the sliding mode control of uncertain systems with single or multiple constant or time varying state delays submitted to additive perturbations the sliding surface is designed so to maximize the calculable set of admissible delays the conditions for the existence of the sliding regime are studied by using lyapunov krasovskii functionals and lyapunov razumikhin functions lmis are used for the optimization procedure two examples illustrate the proposed method

linear complementarity systems we introduce a new class of dynamical systems called linear complementarity systems the time evolution of these systems consists of a series of continuous phases separated by events which cause a change in dynamics and possibly a jump in the state vector the occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming the framework we describe is suitable for certain situations in which both differential equations and inequalities play a role for instance in mechanics electrical networks piecewise linear systems and dynamic optimization we present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions

attractivity theory for second order non smooth dynamical systems with application to dry friction in this paper we study the attractivity properties of the set of stationary solutions for a general class of second order non smooth dynamical system involving friction term sufficient conditions for the local attractivity of the set of stationary solutions are given in the case of dry friction and negative viscous damping an estimation of the attraction domain is also given in this case applications can be found in unilateral mechanics

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

robust sliding mode control for markovian jump singular systems with randomly changing structure abstract this paper discusses the robust optimization by a sliding mode control smc approach for uncertain singular markovian jump smj time varying delay system with nonlinear perturbation which uncertainties occur randomly firstly a different integral type sliding mode surface sms and a different lyapunov krasovskii function are introduced secondly by using linear matrix inequalities sufficient conditions are proposed to ensure the mean square exponentially admissible msea with an h performance level of the unforced uncertain smj time varying delay system in the specified sms next a composed smc law with the parameter uncertainties occurring randomly can ensure the reachability of the predefined sms finally three numerical examples are given to test the feasibility of the theory

conley index condition for asymptotic stability in this paper we use conley index theory to develop necessary conditions for stability of equilibrium and periodic solutions of nonlinear continuous time systems the conley index is a topological generalization of the morse theory which has been developed to analyze dynamical systems using topological methods in particular the conley index of an invariant set with respect to a dynamical system is defined as the relative homology of an index pair for the invariant set the conley index can then be used to examine the structure of the system invariant set as well as the system dynamics within the invariant set including system stability properties efficient numerical algorithms using homology theory have been developed in the literature to compute the conley index and can be used to deduce the stability properties of nonlinear dynamical systems

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 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

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

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

exponential stability of stochastic delay interval systems abstract although deterministic interval systems have received a great deal of attention so far there is no work on stochastic interval systems the main aim of this paper is to initiate the study of stochastic interval systems of course there are many properties of such systems to be investigated but this paper will concentrate on the study of exponential stability of stochastic interval systems with time varying delays the main technique used in this paper is the razumikhin type theorem established recently by mao stochastic process appl 65 1996 233 250

robust h control for linear time invariant systems with norm bounded uncertainty in the input matrix abstract this paper focuses on the problem of robust h control design for a class of linear time invariant systems with uncertainty in the state space model we consider uncertain systems with norm bounded parameter uncertainty in the input matrix the paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an h norm bound constraint on disturbance attenuation paralleling to the theory of robust control the robust h control problem is solved via the notion of quadratic stabilization with an h norm bound constraint necessary and sufficient conditions for quadratic stabilization with an h norm bound are derived it is shown that the solution to this problem involves solving a parameter dependent algebraic riccati equation the results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and h optimal control

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

matrices with identical sets of neighbors given a generic m by n matrix a a lattice point h in n is a neighbor of the origin if the body x ax b with bi max 0 aih i 1 m contains no lattice point other than 0 and h the set of neighbors n a is finite and 0 symmetric we show that if a is another matrix of the same size with the property that sign aih sign ai h for every i and every h e n a then a has precisely the same set of neighbors as a the collection of such matrices is a polyhedral cone described by a finite set of linear inequalities each such inequality corresponding to a generator of one of the cones ci pos h e n a aih 0 computational experience shows that ci has few generators we demonstrate this in the first nontrivial case n 3 m 4

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

robust covariance control for perturbed stochastic multivariable system via variable structure control based on the concept of variable structure control this paper investigates the steady state covariance assignment problem for perturbed stochastic multivariable systems by using the invariance property of variable structure systems the matched perturbation of the system disappears on the sliding mode with the aid of ito formula the controller u t is proposed combining the sliding phase and hitting phase of the system design the control feedback gain matrix g is derived to satisfy the steady state covariance assignment