Requiring only basic knowledge of linear systems and lyapunov stability theory, stability of timedelay systems, 2 nd ed is accessible to a broad audience of researchers, professional engineers, and graduate students. Dwell time stability conditions of the switched delay systems are derived using multiple clockdependent lyapunovkrasovskii functionals. Specifically, the delay occurs not only in the state equation, but also in the switching signal from the controller, which brings the difficulty of controller design to achieve meansquare exponential stabilization. Request pdf switched timedelay systems this chapter is concerned. Finitetime stability analysis of switched genetic regulatory networks yin, lizi, journal of applied mathematics, 2014. Robust control for uncertain switched nonlinear systems with time delay under asynchronous switching, iet control theory and applications 3 8. However, parallel general results for switched timedelay systems are not abundant in the literature. A switched system may be obtained from a hybrid system by. Finitetime control for switched linear systems with. Sliding mode control of discretetime switched systems with. This chapter focuses on the stability analysis problem for a class of continuous time switched time delay systems modelled by delay differential equations. Then, we will derive a necessary and sufficient condition of the stabilization via constructing a quadratic lyapunov function of the form vx xpx 1 the conditions consist of a collection of matrix. The existence of pure time lag, regardless if it is present in the control or and the state, may cause undesirable system transient response, or even instability.
Stabilization of lti switched systems with input time delay. Brief paper dwelltime computation for stability of switched systems. The material contained in this book is not only organized to focus on the new developments in the analysis and control methodologies for such switched time delay systems, but it also integrates the impact of the delay factor on issues such as asymptoticexponential stability, feedback stabilization and control design. Tracking control for time delay switched system is widely. By using the average dwell time approach and the piecewise lyapunov function technique, a sufficient condition is proposed to guarantee the exponential stability of the switched systems with time delays. The timevarying system parameters are assumed to be normbounded. This condition will be fulfilled if and only if r is a stable matrix. In this paper, the problem of sliding mode control of a discretetime switched system with timevarying delay is investigated. It is known that a wide variety of realworld systems are subject to uncertainty and also time delay in their dynamics. The problems of meansquare exponential stability and robust control of switched stochastic systems with time varying delay are investigated in this paper. Both the stable continuous dynamics case and the stable impulsive dynamics case were investigated. Stability analysis of switched time delay systems siam journal on. A switched system is composed of an indexed family of delay subsystems described by continuoustime dynamics and a rule orchestrating the switching between them kotelyanski lemma.
Research article stability analysis and model reduction for. This class of systems is frequently called switched system. Stability results for switched linear systems with constant. Asadinia, ms, binazadeh, t 2017 design of robust control law for stabilization of singular systems with timevarying delay in the presence of. On stability analysis of switched linear time delay systems under arbitrary switching. Pdf a new stability analysis for discretetime switched.
In this paper, stochastic stability was studied for a general class of stochastic impulsive switched timedelay systems. The aim of this study is to find an improved dwell time that guarantees the stability of switched systems with heterogeneous constant timedelays. On stability analysis of switched linear timedelay. In this paper, stochastic stability was studied for a general class of stochastic impulsive switched time delay systems. In this study, the authors analyse the stability of switched positive linear timedelay systems. Delaydependent synchronization for complex dynamical networks with interval timevarying and switched coupling delays botmart, t. Stability results of timedelay switched systems have been obtained recently for the case of one single delay by decomposition of the. Therefore, the stability analysis of switched timedelay systems is very worthy to be researched. Based on the average dwell time method and gronwallbellman inequality, a new meansquare exponential stability criterion of such system is derived in terms of linear matrix inequalities lmis. Researchers from the control and system theory communities have been working with switched systems due to their abilities.
Thus we are interested in continuous time systems with isolated discrete switching events. Switched timedelay systems request pdf researchgate. Nonlinear continuous time systems with a switching. For the statedependentimpulsecase,usingthebequivalentmethod,impulsive switched timedelay. The work in 17 gives the exponential stability criterion for a class of switched linear systems with constant time delay by combining dwelltime with the piecewise lyapunov function. Stability analysis and stabilization of a class of discrete. Stability analysis of switched systems with timevarying. Stability analysis of impulsive switched timedelay. Stability and control switched timedelay systems presents an introductory, yet comprehensive, treatment of. Research article stability analysis and model reduction. Based on the average dwell time method and gronwallbellman inequality, a new meansquare exponential stability criteria and performance analysis are presented. Quadratic stabilization of switched systems with time delay via asynchronous switching consider a switched system with time delay. This paper addresses the stability analysis problem for a class of discretetime switched nonlinear timedelay systems with polytopic uncertainties.
Switched timedelay systems presents an introductory, yet comprehensive, treatment. Piecewise lyapunovkrasovkii functionals are used for each candidate system to investigate the stability of the switched timedelayed system. On delay independent stabilization analysis for a class of switched largescale. Stability of timedelay feedback switched linear systems article in ieee transactions on automatic control 5510. By developing a novel multiple discontinuous copositive lyapunovkrasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under modedependent average dwell time switching. Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. Switched timedelay systems presents an introductory, yet comprehensive, treatment of. Switched time delay systems presents an introductory, yet comprehensive, treatment of. The corresponding conditions are approximated by both using piecewise linear functions and sum of squares polynomials. Stability analysis and stabilization of a class of discretetime nonlinear switched systems with timedelay and affine parametric uncertainty n. Stabilization of switched linear systems with time delay in detection of switching signal, applied mathematics and computation 305 6. Under the assumption that each candidate system is stable for small delay values, a sufficient condition.
This paper deals with the stability of switched systems with timevarying delay. Furthermore, robust controller is designed to guarantee that the corresponding. Stability and control design for time varying systems with time varying delays using a trajectory based approach. When the switched system is not necessarily positive, we first establish a delay independent stability criterion under arbitrary switching signal by using a new method that is different from the. Kotelyanski elaborates a particular lemma, well adapted for stability study when off diagonal elements of matrix are nonnegative. A novel stability analysis of uncertain switched systems.
Delay dependent stability of linear timedelay systems 227 which presents a wellknown lyapunovs equation for the system without timedelay. Stability of switched systems with time delay semantic. Stability analysis for stochastic impulsive switched time. Exponential stabilization for nonlinear switched stochastic.
Hence stability and stabilization problems for switched systems with time delay have. On stability analysis of switched linear timedelay systems. It is the latter point of view that prevails in these notes. Switching controller for stabilization of linear systems with. Switched time delay systems presents an introductory, yet comprehensive, treatment of switched time delay systems by jointly combining two fundamental attributes. The inputtostate stability iss and integral inputtostate stability iiss problems are addressed for a family of impulsive switched hybrid timedelay systems with delayed impulses. It is known that a wide variety of realworld systems are subject to uncertainty and also timedelay in their dynamics. Then, a transformation under the arrow form is employed. A novel stability analysis of uncertain switched systems with. Inputtostate stability of impulsive switched hybrid time. Dwelltime computation for stability of switched systems with. Fault tolerant control of switched nonlinear systems with.
For such two cases, sufficient stability conditions were derived. Stability analysis of switched systems with timevarying discontinuous delays frederic mazenc michael malisoff hitay ozbay 06. Robust stability and control of switched linear systems thesis. In this paper, the problem of sliding mode control of a discrete time switched system with time varying delay is investigated. Indeed, by constructing an appropriated common lyapunov.
Stabilization of switched linear systems with timedelay in detection of switching signal, applied mathematics and computation 305 6. We will first introduce a definition of stabilization of the switched systems with time delay inputs. Dwell timebased stabilisation of switched linear delay. Based on a novel switched time varying lyapunov functional method, some new lmibased sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Razumikhin method, lyapunov functionals approach, and the comparison principle technique, we obtain some improved razumikhin. This class of interconnected subsystems consists of unknown but bounded state delay and nonlinear terms, and each subsystem can be globally stable, unstable, or locally stable. Stability analysis of impulsive switched timedelay systems.
Sliding mode control of discretetime switched systems. Switched timedelay systems stability and control magdi s. Stability analysis for a class of switched nonlinear time. International journal of robust and nonlinear control. Stability results for switched linear systems with. This paper is focused on delay independent stability analysis for a class of switched linear systems with time varying delays that can be unbounded. In this paper, we study the qualitative properties of linear and nonlinear delay switched systems which have stable and unstable subsystems. In this thesis, the stability analysis and control synthesis for uncertain switched timedelay systems are investigated. Using the adt scheme, switching design for exponential stability was proposed in foraclass of switched discrete. Abstract the stability analysis problem is studied in this paper for a class of discretetime switched timedelay systems described by delayed recurrence equations or a state matrix transformed after under the arrow form, by applying the comparison, the aggregations techniques and the mmatrix properties, new asymptotic stability conditions of such systems are derived under arbitrary switching. Stability of switched nonlinear systems with delay and.
Tracking control for timedelay switched system is widely. Stability of switched positive linear timedelay systems. The time varying system parameters are assumed to be normbounded. This paper presents an approach to the stability analysis of a class of nonlinear interconnected continuous. Thus, it is necessary to investigate finite time stability and finite time boundedness for a class of switched linear systems with time varying delay, which is an important property for switched system. Stability analysis of switched time delay systems siam. Furthermore, basedonadtmethod,in the stability of switched systems with stable and unstable subsystems co existing was considered. The material contained in this book is not only organized to focus on the new developments in the analysis and control methodologies for such switched timedelay systems, but it also integrates the impact of the delay factor on issues such as asymptoticexponential stability, feedback stabilization and control design. In this paper, the exponential stability analysis and robust control for switched stochastic time delay systems have been investigated. Delaydependent stability analysis for discretetime switched linear. Delayindependent stability of switched linear systems. Stability analysis and robust control of switched stochastic. First, we prove some inequalities which lead to the switching laws that guarantee. This paper addresses the stability analysis problem for a class of discrete time switched nonlinear time delay systems with polytopic uncertainties.
This paper deals with the stability of switched systems with time varying delay. This case is often encountered in the networked control systems ncs. Dynamics of delayed switched nonlinear systems with applications. The existence of pure time lag, regardless if it is present in the control orand the state, may cause undesirable system transient response, or even instability. The work in 17 gives the exponential stability criterion for a class of switched linear systems with constant time delay by combining dwell time with the piecewise lyapunov function. The paper investigates meansquare exponential stabilization for a class of nonlinear switched stochastic systems with interval time varying delay under asynchronous switching. Stability analysis and controller design switched time. Based on a novel switched timevarying lyapunov functional method, some new lmibased sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Switching controller for stabilization of linear systems. Xiong, krasovskii and razumikhin stability theorems for stochastic switched nonlinear timedelay systems, siam journal on control and optimization, 2019, 572. Switched timedelay systems presents an introductory, yet comprehensive, treatment of switched timedelay systems by jointly combining two fundamental attributes. Stability analysis and controller design switched timedelay. Employing the multiple lyapunovkrasovskii functionals method, sufficient conditions are established guaranteeing the issiiss property of the given system. The main challenge in a switched control system is the sta bility analysis.
Stability analysis and stabilization of a class of. The stabil ity of discretetime systems with time varying delays can be analyzed by using. These considered systems are characterized by delayed difference nonlinear equations which are given in the state form representation. The main issues then become stability analysis and control synthesis. Stability of switched systems with average dwelltime. Switching controller for stabilization of linear systems with switched timevarying delays wenjuan jiang, emilia fridman, alexandre kruszewski and jeanpierre richard abstractthis paper considers interval timevarying delay systems with delayed estimation of the delay. In the interests of brevity, only single delay is studied in this paper, but it can be extended to the case.
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