switched nonlinear systems with state dependent dwell time the asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied the system switches among a family of integral input to state stable systems the time between two consecutive switchings is not less than a value d this dwell time d is allowed to take different values according to a function whose argument is the state of the system at the switching times we propose a dwell time function which depends on the comparison functions which characterize the integral input to state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with bounded energy the main feature of the analysis is that it does not rely on the property for the switching to stop in finite time the two important cases of locally exponentially stable and feedforward systems are analyzed in detail

representation of certain homogeneous hilbertian operator spaces and applications following grothendieck s characterization of hilbert spaces we consider operator spaces f such that both f and f completely embed into the dual of a c algebra due to haagerup musat s improved version of pisier shlyakhtenko s grothendieck inequality for operator spaces these spaces are quotients of subspaces of the direct sum c r of the column and row spaces the corresponding class being denoted by qs c r we first prove a representation theorem for homogeneous f qs c r starting from the fundamental sequences phi c n bigg sum k 1 ne k1 otimes e k bigg c otimes min f 2 quad mbox and quad phi r n bigg sum k 1 ne 1k otimes e k bigg r otimes min f 2 given by an orthonormal basis ek of f under a mild regularity assumption on these sequences we show that they completely determine the operator space structure of f and find a canonical representation of this important class of homogeneous hilbertian operator spaces in terms of weighted row and column spaces this canonical representation allows us to get an explicit formula for the exactness constant of an n dimensional subspace fn of f mathit ex f n sim biggl frac n phi c n phi r bigg frac phi c n phi r n bigg frac n phi r n phi c bigg frac phi r n phi c n bigg biggr 1 2 in the same way the projection injectivity constant of fn is explicitly expressed in terms of c and r too orlicz space techniques play a crucial role in our arguments they also permit us to determine the completely 1 summing maps in effros and ruan s sense between two homogeneous spaces e and f in qs c r the resulting space 1o e f isomorphically coincides with a schatten orlicz class s moreover the underlying orlicz function is uniquely determined by the fundamental sequences of e and f in particular applying these results to the column subspace cp of the schatten p class we find the projection and exactness constants of cpn and determine the completely 1 summing maps from cp to cq for any 1 p q

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

finite time boundedness and l2 gain analysis for switched delay systems with norm bounded disturbance abstract finite time boundedness and finite time weighted l 2 gain for a class of switched delay systems with time varying exogenous disturbances are studied based on the average dwell time technique sufficient conditions which guarantee the switched linear system with time delay is finite time bounded and has finite time weighted l 2 gain are given these conditions are delay dependent and are given in terms of linear matrix inequalities detail proofs are given by using multiple lyapunov like functions an example is employed to verify the efficiency of the proposed method

the generalized riemann problem for reactive flows abstract a generalized riemann problem is introduced for the equations of reactive non viscous compressible flow in one space dimension initial data are assumed to be linearly distributed on both sides of a jump discontinuity the resolution of the singularity is studied and the first order variation in time of flow variables is given in exact form

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

embedding of the operator space oh and the logarithmic little grothendieck inequality we use voiculescu s concept of free probability to construct a completely isomorphic embedding of the operator space oh in the predual of a von neumann algebra we analyze the properties of this embedding and determine the operator space projection constant of oh n frac 1 108 sqrt frac n 1 ln n le inf p mathcal b ell 2 to oh n p 2 p left p right cb le 288 pi sqrt frac 2n 1 ln n the lower estimate is a recent result of pisier and shlyakhtenko that improves an estimate of order 1 1 lnn of the author the additional factor 1 sqrt 1 ln n indicates that the operator space oh n behaves differently than its classical counterpart ell 2 n we give an application of this formula to positive sesquilinear forms on mathcal b ell 2 this leads to logarithmic characterization of c algebras with the weak expectation property introduced by lance

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

stabilization of persistently excited linear systems by delayed feedback laws this paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback where we suppose that the feedback law is not applied instantaneously but after a certain positive delay not necessarily constant the main result is that under certain spectral hypotheses on the linear system stabilization by means of a linear delayed feedback is indeed possible generalizing a previous result already known for non delayed feedback laws

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

delay dependent criteria for global robust periodicity of uncertain switched recurrent neural networks with time varying delay in this paper we introduce some ideas of switched systems into the field of neural networks and a large class of switched recurrent neural networks srnns with time varying structured uncertainties and time varying delay is investigated some delay dependent robust periodicity criteria guaranteeing the existence uniqueness and global asymptotic stability of periodic solution for all admissible parametric uncertainties are devised by taking the relationship between the terms in the leibniz newton formula into account because free weighting matrices are used to express this relationship and the appropriate ones are selected by means of linear matrix inequalities lmis the criteria are less conservative than existing ones reported in the literature for delayed neural networks with parameter uncertainties some examples are given to show that the proposed criteria are effective and are an improvement over previous ones

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

observer design for switched recurrent neural networks an average dwell time approach this paper is concerned with the problem of observer design for switched recurrent neural networks with time varying delay the attention is focused on designing the full order observers that guarantee the global exponential stability of the error dynamic system based on the average dwell time approach and the free weighting matrix technique delay dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities the error state decay estimate is also given then the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results finally four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods

exponential stability results for uncertain neutral systems with interval time varying delays and markovian jumping parameters abstract this paper deals with the global exponential stability analysis of neutral systems with markovian jumping parameters and interval time varying delays the time varying delay is assumed to belong to an interval which means that the lower and upper bounds of interval time varying delays are available a new global exponential stability condition is derived in terms of linear matrix inequality lmi by constructing new lyapunov krasovskii functionals via generalized eigenvalue problems gevps the stability criteria are formulated in the form of lmis which can be easily checked in practice by matlab lmi control toolbox two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

model reduction by nice selections for linear switched systems a moment matching method for model reduction of linear switched systems lsss is presented the method can be seen as a non trivial extension of the krylov subspace methods for linear time invariant lti systems the procedure is based on the so called nice selections which represent a choice of basis in the reachability or observability space of the lss the framework can also be used for exact matching of the input output behavior of an lss with a reduced order lss for a specific switching sequence conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples

technical communique improved ellipsoidal bound of reachable sets for time delayed linear systems with disturbances we consider the problem of finding an ellipsoidal reachable set that bounds the states of time delayed linear systems with bounded peak disturbances the considered time delay is time varying but it has an upper bound in magnitude and rate based on the modified lyapunov krasovskii l k type functional we derive a delay dependent result expressed in the form of matrix inequalities containing only one non convex scalar the result is extended to uncertain time delayed linear systems finally we show the usefulness of our result by a comparative numerical example

passivity of switched recurrent neural networks with time varying delays this paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time varying delays first using the multiple lyapunov functions method a state dependent switching law is designed to present a stochastic passivity condition second a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state dependent switching third based on the average dwell time approach a class of switching signals is determined to guarantee the switched neural network stochastically passive finally three numerical examples are provided to illustrate the characteristics of three proposed switching laws

a new result on h_ infty state estimation of delayed static neural networks this brief presents a new guaranteed h infty performance state estimation criterion for delayed static neural networks to facilitate the use of the slope information about activation function the estimation error of activation function is separated into two parts for the first time then a novel lyapunov krasovskii functional lkf is constructed which has fully captured the slope information of the activation based on the new lkf a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with h infty performance the desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem the simulation results show that the proposed method has much better performance than the most recent results

external stability of switching control systems abstract this paper investigates external stability defined by the normal l 2 norm of switching control systems it proposes definitions of the maximum minimum dwell time for switching systems and then derives an important relation between the number of switchings and the maximum minimum dwell time applying this relation it establishes criteria on external stability of switching control systems consisting of hurwitz stable subsystems furthermore a switching law is proposed and is proven to be realizable given this proposed switching law and applying the previous derived relation the switching control systems comprised of both hurwitz stable and hurwitz unstable subsystems are proved to be externally stable

optimal control of switched systems based on parameterization of the switching instants this paper presents a new approach for solving optimal control problems for switched systems we focus on problems in which a prespecified sequence of active subsystems is given for such problems we need to seek both the optimal switching instants and the optimal continuous inputs in order to search for the optimal switching instants the derivatives of the optimal cost with respect to the switching instants need to be known the most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state costate stationarity equations the boundary and continuity conditions along with their differentiations this method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed an extension of the method is also applied to problems with internally forced switching examples are shown to illustrate the results in the paper

adaptive fuzzy output feedback dynamic surface control of mimo switched nonlinear systems with unknown gain signs this paper investigates the problem of adaptive fuzzy tracking control for a class of multi input multi output mimo switched uncertain nonlinear systems with unknown gain signs and unmeasurable states fuzzy logic systems are used to approximate the unknown nonlinear functions a fuzzy mimo switched observer is designed to estimate the unmeasurable states the nussbaum type functions are utilized to handle the unknown gain signs of the system under study a switched dynamic surface based adaptive fuzzy control approach is then established by exploiting the average dwell time method and backstepping and the dynamic surface control technique which constructs multiple switched first order filters to overcome the multiple explosion of complexity problem when applying the backstepping recursive design scheme also the proposed approach extends the classical dynamic surface control technique from its original non switched nonlinear version to a switched nonlinear version it is proved that all the signals in the closed loop system are semiglobal uniformly ultimately boundedness under a class of switching signals with average dwell time and the tracking errors converge to a small neighborhood of the origin a mass spring damper system with controller switching as a practical example is provided to demonstrate the effectiveness of the proposed design method

embedding of cq and rq into noncommutative lp spaces 1 p q 2 we prove that a quotient of a subspace of cp prp 1 p 2 embeds completely isomorphically into a noncommutative lp space where cp and rp are respectively the p column and p row hilbertian operator spaces we also represent cq and rq p q 2 as quotients of subspaces of cp prp consequently cq and rq embed completely isomorphically into a noncommutative lp m we further show that the underlying von neumann algebra m cannot be semifinite

robust reliable stabilization of uncertain switched neutral systems with delayed switching this paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm bounded a state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems and the dwell time approach is utilized for the stability analysis and controller design a numerical example is given to illustrate the effectiveness of the proposed method

finite time control of interconnected impulsive switched systems with time varying delay in this paper the problem of finite time control is addressed for a class of interconnected impulsive switched systems with time varying delay and dynamical disturbance the concepts of finite time stability and finite time boundedness are extended to interconnected impulsive switched systems respectively by resorting to the average dwell time approach and constructing an appropriate lyapunov krasovskii functional some sufficient criteria are provided to cope with the problems of finite time boundedness and finite time stability then based on the decentralized switched control scheme a state feedback controller is established to ensure the finite time stability and the finite time boundedness finally an example and simulation result are demonstrated to illustrate the correctness and effectiveness of the proposed method

travelling waves and finite propagation in a reaction diffusion equation abstract we study the existence of travelling wave solutions and the property of finite propagation for the reaction diffusion equation ut um xx un x t r 0 with m 1 0 n r and u u x t 0 we show that travelling waves exist globally only if m n 2 and only for velocities c c 2 m in the study of propagation we must take into account that solutions of the cauchy problem can be nonunique for n c 0 for m n 2 maximal solutions propagate instantly to the whole space if n

brief paper asymptotic rejection of asymmetric periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns this class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form some disturbances which are generated from nonlinear oscillation such as van de pol oscillators as well as disturbances with symmetric half period wave forms such as sinusoidal disturbances and triangular disturbances etc the systems considered in this paper can be transformed to the nonlinear output feedback form the amplitude and phase of the disturbances are unknown the novel concept of integral phase shift is introduced together with the newly introduced half period integration operator to investigate the invariant properties of asymmetric periodic disturbances they are used for the estimation of unknown disturbances in the systems together with observer design techniques to deal with nonlinearity the proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance and ensures the overall stability of the system

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

a geometric approach for reachability and observability of linear switched impulsive systems abstract this paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices first some new concepts with respect to the reachability and unobservability are introduced especially span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces then the geometric characterization of the span reachable and unobservable sets is presented moreover the relations between the span reachable set unobservable set and the invariant subspaces of such systems are discussed finally corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

dwell time based stabilisation of switched delay systems using free weighting matrices abstractin this paper we present a quasi convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems piecewise lyapunov krasovskii functionals are introduced and the upper bound for the derivative of lyapunov functionals is estimated by free weighting matrices method to investigate non switching stability of each candidate subsystems then a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system once these conditions are represented by a set of linear matrix inequalities dwell time optimisation problem can be formulated as a standard quasi convex optimisation problem numerical examples are given to illustrate the improvements over previously obtained dwell time bounds using the results obtained in the stability case we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers the algorithm solves the problem with successive linearisation of nonlin

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

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

existence and uniqueness of solutions of reaction convection equations with non lipschitz nonlinearity abstract in this work we study single balance law u t u f u with bounded initial value and find that there may exist maximal and minimal solutions if f u is not lipschitz continuous at u 0 we also show that comparison principle is valid for such solutions and the solutions may blow up or not under certain conditions it is determined by the strength of source supply as well as the competition between the source and flux

further result on guaranteed h_ infty performance state estimation of delayed static neural networks this brief considers the guaranteed h infty performance state estimation problem of delayed static neural networks an arcak type state estimator which is more general than the widely adopted luenberger type one is chosen to tackle this issue a delay dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed h infty performance it is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities compared with some previous results much better performance is achieved by our approach which is greatly benefited from introducing an additional gain matrix in the domain of activation function an example is finally given to demonstrate the advantage of the developed result

brief digital optimal reduced order control of pulse width modulated switched linear systems in this paper digital optimal control of pulse width modulated switched linear systems is considered the equivalent discrete time system and its deviation around a stationary solution plays an important role an optimal linear discrete time deviation controller is developed the controller is chosen to be one step ahead predictive which is a natural choice for control of digital pulse modulated systems the controller is optimal i e a cost criterion is minimized the theory is generally applicable and gives in principle a tool to design a digital optimal controller for an arbitrary pulse width modulated switched linear system the theory is illustrated by examples from the field of switched electrical networks

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

on delay dependent stability for a class of nonlinear stochastic systems with multiple state delays abstract global asymptotic stability conditions for nonlinear stochastic systems with multiple state delays are obtained based on the convergence theorem for semimartingale inequalities without assuming the lipschitz conditions for nonlinear drift functions the lyapunov krasovskii and degenerate functionals techniques are used the derived stability conditions are directly expressed in terms of the system coefficients nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given

effects of mixed modes on the stability analysis of switched time varying delay systems a phenomenon known as mixed mode occurs naturally in switched delay systems and it makes the stability analysis for such systems a challenge especially for the case of time varying delays this note aims to investigate the effects of mixed modes on the stability analysis of switched time varying delay systems which are motivated from networked control applications by constructing a lyapunov krasovskii functional and using the estimation of quadrature as well as the average dwell time approach new exponential stability conditions are given for the switched time varying delay systems with both stable and unstable subsystems this can be seen as a generalization of existing results that mainly focus on the cases of constant delay and all stable subsystems finally simulation examples are presented to illustrate the developed results

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

delay independent stabilization of a class of time delay systems via periodically intermittent control the problem of delay independently periodically intermittent stabilization for a class of time delay systems is examined first the stability of the considered periodically intermittently controlled time delay systems is analyzed by using the piecewise switching time dependent lyapunov function functional the introduced lyapunov function functional is nonincreasing at switching instants which can guarantee the exponential stability of the considered systems irrespective of the sizes of the state delays next based on the newly established stability criteria sufficient conditions for the existence of delay independently periodically intermittent state feedback controllers are derived finally two illustrative examples are presented to show the validity of the obtained results

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

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

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

exponential synchronization of neural networks with discrete and distributed delays under time varying sampling this paper investigates the problem of master slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals an improved method is proposed which captures the characteristic of sampled data systems some delay dependent criteria are derived to ensure the exponential stability of the error systems and thus the master systems synchronize with the slave systems the desired sampled data controller can be achieved by solving a set of linear matrix inequalitys which depend upon the maximum sampling interval and the decay rate the obtained conditions not only have less conservatism but also have less decision variables than existing results simulation results are given to show the effectiveness and benefits of the proposed methods

well posedness analysis of switch driven piecewise affine systems the well posedness problem existence and uniqueness of solutions of a class of multi modal piecewise affine systems is addressed where binary switches individually act under autonomous switching first a new transition rule on the discrete state called the switch based transition rule is introduced and some relations with the mode based transition rule are discussed next a sufficient condition for such a multi modal system to be well posed for all external inputs is derived in terms of well posedness of its subsystems of lower complexity bimodal systems finally an easily checkable condition for the bimodal system to be well posed for all external inputs is given which consequently allows us to algebraically determine well posedness of the multi modal systems in question

robust state dependent switching of linear systems with dwell time a state dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty a lyapunov function in quadratic form is assigned to each subsystem such that it is non increasing at the switching instants during the dwell time this function varies piecewise linearly in time after the dwell the system switches if the switching results in a decrease in the value of the lf the method proposed is also applicable to robust stabilization via state feedback it is further extended to guarantee a bound on the l2 gain of the switching system it is also used in deriving state feedback control law that robustly achieves a prescribed l2 gain bound

delay dependent hbox h _ infty filter design for discrete time fuzzy systems with time varying delays this paper investigates delay dependent hinfin filter design problems for discrete time fuzzy systems with time varying delays first a novel delay dependent piecewise lyapunov krasovskii functional ddplkf is proposed in which both the upper bound of delays and the delay interval are considered based on this ddplkf the delay dependent stability criteria for discrete time systems with constant or time varying delays are obtained respectively then delay dependent full order and reduced order hinfin filter design approaches are proposed the filter parameters can be obtained by solving a set of linear matrix inequalities lmis simulation examples are also given to illustrate the performance of the proposed approaches it is shown that our approaches are less conservative and that the corresponding hinfin filters can achieve better performance than the existing approaches

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

brief paper periodic stabilizability of switched linear control systems stabilizability via direct observer based state feedback control for discrete time switched linear control systems slcss is investigated in this paper for an slcs the control factors are not only the control input but also the switching signal and they need to be designed in order to stabilize the system as a result stabilization design for slcss is more complicated than that for non switched ones differently from the existing approaches a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems it is highlighted that multiple feedback controllers need to be designed for one subsystem for discrete time slcss it is proved that reachability implies periodic stabilizability via state feedback a necessary and sufficient criterion for periodic stabilizability is also established two stabilization design algorithms are presented for real application moreover it is proved that reachability and observability imply periodic stabilizability via observer based feedback for discrete time slcss periodic detectability as the dual concept of periodic stabilizability is discussed and the stabilization design algorithms via observer based feedback are presented as well

completely p summing maps on the operator hilbert space oh abstract we prove the completely p summing ideals of oh are all equal as sets for 1 p 2 a phase transition then occurs at p 2 as we also show for p 2 the completely p summing ideals of oh turn out as sets to be schatten ideal classes with the limiting case being the schatten 4 class ideal s 4 when p

μ dependent model reduction for uncertain discrete time switched linear systems with average dwell time in this article the model reduction problem for a class of discrete time polytopic uncertain switched linear systems with average dwell time switching is investigated the stability criterion for general discrete time switched systems is first explored and a dependent approach is then introduced for the considered systems to the model reduction solution a reduced order model is constructed and its corresponding existence conditions are derived via lmi formulation the admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential h performance a numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results

on weak invariance principles for nonlinear switched systems in this technical note we develop two weak invariance principles for nonlinear switched systems we first present a union weak invariance principle for switched systems which includes as a special case the integral invariance principle it is shown that the switched solution approaches the largest weakly invariant set of the combined zero loci of the output functions then we extend the union weak invariance principle to an intersection weak invariance principle which greatly reduces the convergence region unlike the existing results in which the constructions of lyapunov functions are inevitable our principles do not require the existence of lyapunov functions numerical examples are presented to demonstrate the feasibility of our principles as well as applications to multi agent consensus problems

a maurey type result for operator spaces the little grothendieck theorem for banach spaces says that every bounded linear operator between c k and l2 is 2 summing however it is shown in m junge embedding of the operator space oh and the logarithmic little grothendieck inequality invent math 161 2 2005 225 286 that the operator space analogue fails not every cb map v k oh is completely 2 summing in this paper we show an operator space analogue of maurey s theorem every cb map v k oh is q cb summing for any q 2 and hence admits a factorization v x c q v cb axb q with a b in the unit ball of the schatten class s2q

exponential stability on stochastic neural networks with discrete interval and distributed delays this brief addresses the stability analysis problem for stochastic neural networks snns with discrete interval and distributed time varying delays the interval time varying delay is assumed to satisfy 0 d1 d t d2 and is described as d t d 1 h t with 0 h t d 2 d 1 based on the idea of partitioning the lower bound d 1 new delay dependent stability criteria are presented by constructing a novel lyapunov krasovskii functional which can guarantee the new stability conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results

technical communique robust reliable control for a class of uncertain nonlinear state delayed systems this paper deals with the problem of robust reliable control design for a class of nonlinear uncertain state delayed systems the system under consideration involves state time delay parameter uncertainties and unknown nonlinear disturbances the nonlinearities are assumed to satisfy the boundedness condition and the parameter uncertainties are allowed to be time varying unstructured the purpose of this problem is to design the state feedback controller such that for all admissible uncertainties as well as actuator failures occuring among a prespecified subset of actuators the plant remains globally exponentially stable independently of the time delay an effective modified algebraic riccati equation approach is developed to solve the problem addressed it is shown that designed nonlinear time delay control systems provide guaranteed robust reliable stability despite possible actuator failures we present an illustrative example to demonstrate the applicability of the proposed design approach

reachability and observability reduction for linear switched systems with constrained switching we present an algorithm for reducing the number of continuous states of a discrete time linear switched system such that the reduced system has the same input output behavior as the original system for a subset of switching sequences the procedure can be interpreted as reachability and observability reduction for a linear switched system with constrained switching the proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems

distributed non fragile filtering in sensor networks with energy constraints this paper investigates the distributed filtering problem for sensor networks with energy constraint and filter gain variation firstly two strategies are proposed to reduce energy consumption i e the measurement size and the transmission rate reduction strategies to reduce the measurement size a useful measurement selection policy is introduced to choose which element of local measurements is transmitted the selected measurement which has a smaller size than the original one is then stochastically transmitted in order to reflect the imprecision in filter implementation the additive filter gain variation problem is considered based on the switched system approach and some stochastic system analysis methods a sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and a prescribed h performance level is guaranteed filter gains are shown to be determined by solving a set of linear matrix inequalities lmis finally a simulation example is given to demonstrate the effectiveness of the proposed design

delay dependent stability for recurrent neural networks with time varying delays this brief is concerned with the stability for static neural networks with time varying delays delay independent conditions are proposed to ensure the asymptotic stability of the neural network the delay independent conditions are less conservative than existing ones to further reduce the conservatism delay dependent conditions are also derived which can be applied to fast time varying delays expressed in linear matrix inequalities both delay independent and delay dependent stability conditions can be checked using the recently developed algorithms examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

stabilization for switched stochastic neutral systems under asynchronous switching in this paper the mean square exponential stability of switched stochastic neutral systems with time varying delay under asynchronous switching is investigated a new lyapunov function dependent on the controllers switching signal is constructed which can counteract the difficulty of controller design to stabilize the system under asynchronous switching moreover the value of the lyapunov function is allowed to increase during mismatched periods based on the average dwell time approach a sufficient condition expressed by a set of linear matrix inequalities lmis is derived to guarantee the mean square exponential stability for the closed loop system and the controllers with asynchronous switching are designed finally a numerical example illustrates the effectiveness of the results

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

delay independent criteria for exponential admissibility of switched descriptor delayed systems this paper deals with the uniform exponential admissibility problem for switched descriptor systems with time varying delays a criterion for regularity impulsiveness free of each subsystem is presented a solution to switching impulsiveness free for switched descriptor systems is provided a novel type of piecewise lyapunov functionals is introduced this type of lyapunov functionals can efficiently overcome the switching jump of adjacent lyapunov functionals at switching times by applying this type of lyapunov functionals and algebraic manipulations the delay independent conditions for uniform exponential admissibility is established on the minimum dwell time

stability of uncertain piecewise affine systems with time delay delay dependent lyapunov approach this article addresses the problem of robust stability of piecewise affine pwa uncertain systems with unknown time varying delay in the state it is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available a set of linear matrix inequalities lmis is derived providing sufficient conditions for the stability of the system these conditions depend on the upper bound of the delay the main contributions of the article are as follows first new delay dependent lmi conditions are derived for the stability of pwa time delay systems second the stability conditions are extended to the case of uncertain pwa time delay systems numerical examples are presented to show the effectiveness of the approach

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems

l 2 gain analysis and control synthesis of uncertain discrete time switched linear systems with time delay and actuator saturation the problem of l 2 gain analysis and control synthesis is studied for a class of uncertain discrete time switched linear systems with time delay and saturating actuators by using the multiple lyapunov functions method with the state feedback controllers adopted beforehand an analysis condition on disturbance tolerance is derived under which the operating state trajectory with zero initial condition will remain inside a bounded set in its proximity then with this condition at hand the largest disturbance tolerance level is determined via the solution of a constrained optimisation problem then a sufficient condition for the restricted l 2 gain over the set of tolerable disturbances is derived the smallest upper bound on the restricted l 2 gain is also obtained by solving a constrained optimisation problem furthermore when controller gain matrices are design variables these optimisation problems are adjusted for solving the control design task an illustrative numerical example is given to demonstr

state estimation for delayed neural networks in this letter the state estimation problem is studied for neural networks with time varying delays the interconnection matrix and the activation functions are assumed to be norm bounded the problem addressed is to estimate the neuron states through available output measurements such that for all admissible time delays the dynamics of the estimation error is globally exponentially stable an effective linear matrix inequality approach is developed to solve the neuron state estimation problem in particular we derive the conditions for the existence of the desired estimators for the delayed neural networks we also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities lmis finally it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks numerical examples are included to illustrate the applicability of the proposed design method

on delay dependent stability for vector nonlinear stochastic delay difference equations with volterra diffusion term global asymptotic stability conditions for discrete vector nonlinear stochastic systems with state delay and volterra diffusion term are obtained based on the convergence theorem for semimartingale inequalities without assuming the lipschitz conditions for nonlinear drift functions the derived stability conditions are directly expressed in terms of the system coefficients a number of nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given the obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

exponential stability of descriptor systems with large delay period based on a switching method this paper addresses the problem of exponential stability for a class of descriptor systems with interval time varying delays the time varying delays contain a large delay period ldp which is often present in practical control systems such descriptor system with ldp has been modeled as a switched descriptor system with delay which may include an unstable subsystem caused by large delay bound by adopting the switching technique and constructing a novel lyapunov krasovskii functional stability criteria are proposed under the restriction frequency and the rate of ldp to ensure that the descriptor system is regular impulse free and exponentially stable finally an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method