Although the last decade has witnessed significant advances in control theory for finite and infinite dimensional systems, the stability and control of timedelay systems have not been fully investigated. 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. Robust sliding mode control for uncertain time delay systems shaocheng qu xiaoyan wang meijing gong hao qu department of information and technology, huazhong normal university, wuhan 430079, p. The main disadvantages of ncss are the network effects that in. Stability of timedelay systems control engineering gu, keqin, kharitonov, vladimir l. Sename grenoble inp timedelay systems 10th september 2014 107. Analysis, observation and control of timedelay systems. It is the latter point of view that prevails in these notes. Stability of discretetime systems with timevarying. Stability and control of timedelay systems springerlink. Delay independent stability of linear switching systems.
Stability results for switched linear systems with constant discrete delays m. Rich results have been obtained on this topic using various approaches and techniques. Stability analysis and robust control of time delay systems wu, min, he, yong, she, jinhua on. Egorov saintpetersburg state university, saintpetersburg, russia email. Stability analysis and robust control of timedelay. Equivalence between lyapunov and scaled smallgain conditions jianrong zhang. The interest in this class of systems has been motivated traditionally by sampleddata systems in which a process is sampled periodically and then controlled via a computer.
However, time delays are present signi cantly in these measurements. This paper deals with linear time invariant systems with multiple delays. With this aim, the paper presents a power system model based on delay differential algebraic equations ddae and describes a general technique. Summary this article addresses the problem of finite. First, a new global stabilizability concept with respect. The main interest in the study of this chapter is the robust stability analysis of feedback control systems, as the one depicted in figure 1, whose main process is represented by an interval plant, with time. Abstract stability analysis and controller design for switched timedelay systems kaveh moezzi madani, concordia unviersity, 2009 in this thesis, the stability analysis and control synthesis for uncertain switched. The interest in this class of systems has been motivated traditionally by sampleddata. New results on stability of discretetime systems with time. In this paper, the stabilization problem of switched control systems with time delay is investigated for both linear and nonlinear cases. Delaydependent lmibased criteria are proposed to achieve the design of switching signal and control.
In this special issue, most papers are concerned with the stability analysis and control problems of timedelay systems. Simple stability conditions of linear discrete time systems with multiple delay sreten b. The fact that some delays can be short and some can be long makes system analysis and control design much more complex. Anghel abstractthe paper describes the impact of timedelays on smallsignal angle stability of power systems. In view of all these, we consider that the stability of switched largescale time delay systems needs to be thoroughly studied.
A new necessary and sufficient stability condition for linear. The primary motivation for designing strict positive real controllers is application to positive real plants. However, most of them is about lyapunov stability 10, 11, but. However, time delays are present signi cantly in these measurements due to transmission channels 3. Stability of switched systems with time delay yi zhanga, xinzhi liub. We present a necessary and su cient stability condition, expressed in terms of the delay lyapunov matrix.
Networked control systems ncss are control systems in which the control loop is closed over a realtime network. The stability problem of timedelay systems has been investigated intensively during the past decades. Control and stability analyzing of the timedelay systems with timevarying delays daniel gontkovic, r. This paper addresses the asymptotic stability of switched time delay systems with heterogeneous time invariant time delays. The timedelay is assumed to be a timevarying continuous function belonging to an interval possibly excluding zero with a bound on its derivative.
Stability and stabilization of systems with time delay limitations and opportunities r. Stability analysis and control of discretetime systems with. Introduction recently, there has been considerable research on switched impulsive systems with time delay. China abstract the problem of robust sliding mode control smc for uncertain time delay systems is investigated in this paper. Robust sliding mode control for uncertain time delay systems. Time delays arises in a wide variety of physical systems and their effects on stability have been carefully investigated in several engineering applications, such as signal processing and circuit design 14. It is widely believed that delays are harmful for robotic systems in terms of stability and performance.
Although the last decade has witnessed significant advances in control theory for finite and infinite dimensional systems, the stability and control of time delay systems have not been fully investiga. This thesis is concerned with the stability, sliding mode control and state estimation problems of time delay systems. Control and stability of the timedelay linear systems. Ibeas2 1 department of electricity and electronics, faculty of science and technology, university of the basque country, campus of leioa bizkaia, p. Abstract stability analysis and controller design for switched time delay systems kaveh moezzi madani, concordia unviersity, 2009 in this thesis, the stability analysis and control synthesis for uncertain switched. Maurer2 1department of electrical and electronic engineering, imperial college london 2institut fur. Global stabilization of switched control systems with time. Optimal control problems with time delays andrea boccia1 p. This paper deals with the stability of a class of linear time varying systems with multiple delays. Stability results for switched linear systems with. On another front of research, positive real theory has played a major role in stability and systems theory 7, 81.
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. Using the lyapunov function method, we give sufficient delay dependent conditions for the exponential stability with a given convergence rate, which are described in terms of linear matrix inequalities lmi and the solution of riccati differential equations rde. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material which, up until now, has been scattered in technical journals and conference proceedings. Recently, stability analysis of timedelay systems has received much attention. The stability analysis problem is studied in this paper for a class of discretetime switched timedelay systems. In this special issue, most papers are concerned with the stability analysis and control problems of time delay systems. Stability analysis for discretetime switched timedelay. Gu october 25, 2010 control systems often operate in the. Mar 02, 2018 stability, control and application of timedelay systems. Time delay system, time delay approximation, polynomial method, lq control. Stability of a class of linear switching systems with time.
Integrating and unstable systems petr dostal, franti ek gazdo, and vladimir bobal faculty of applied informatics, tomas bata university in zlin nad stran mi 4511, 760 05 zlin 5, czech republic 1. Since these biological systems can be modeled as switching systems 15, 16 and many of the applications of switching systems involve control, it is natural to consider the e. New delay dependent stability criteria for linear systems with time varying delay. In fact, the system stability and convergence properties are strongly affected by time delays, which are. However, most of them is about lyapunov stability 10, 11, but not practical stability. By using a newly constructed lyapunov functional and the average dwell time scheme, a. Introduction the presence of a time delay is a common property of many technological processes. Simple stability conditions of linear discrete time. Among them, five papers investigate the simplified or improved stability criteria of time. In this paper we have established a new lyapunovkrasovskii method for linear discrete time systems with multiple time delay. Pdf stability and performance analysis of timedelayed. In view of all these, we consider that the stability of switched largescale timedelay systems needs to be thoroughly studied.
Stability and stabilization of systems with time delay. Among them, five papers investigate the simplified or improved stability criteria of time delayed systems. Stability interval for timevarying delay systems yassine ariba, fr. A new necessary and sufficient stability condition for. This is especially important for control systems where actuators, sensors and transmission lines may introduce time lags 15. Delays exist universally in engineering systems, such as. Many problems exist in this field that are still unresolved, and there is a tendency for the numerical. New delay dependent stability criteria for linear systems. Thus we are interested in continuoustime systems with isolated discrete switching events. Stability of timedelay systems with nonsmall delay fred.
Stability analysis and controller design switched timedelay. Delaydependent stability control for power system with. Switching controller for stabilization of linear systems with. A stability condition with delaydependence for a class of. Timedelay systems based on sliding mode control junsheng wu, zhengxin weng, zuohua tian and songjiao shi fault tolerant control for. Graphical method for robust stability analysis for time. This monograph is a selfcontained, coherent presentation of the background and progress of the stability of timedelay systems. Stability analysis and robust control of time delay systems. The stability of timedelay systems has been well known to be a fundamental. In this paper, we intend to use the time switched method and the comparison theorem to derive a sufficient stability conditions with delay dependence for the switched largescale time delay 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 timedelay systems, but it also integrates. Plants with a time delay cannot often be controlled by conventional controllers designed without consideration of the dead time. Equivalence between lyapunov and scaled smallgain conditions jianrong zhang, carl r. Issn published by world academic press, world academic union 17467659, england, uk journal of information and computing science vol.
Stability analysis and robust control of timedelay systems. Stability analysis and controller design switched time. Stability analysis of switched time delay systems siam. On another front of research, positive real theory has played a major role in stability and. Stability analysis for timedelay systems has attracted many researchers in recent years due to its importance in several practical control systems see e. Robust stability of timedelay systems how to account for uncertain delays. Simple stability conditions of linear discrete time systems. Stability of networked control systems with uncertain time. Delay dependent stability control for power system with multiple time delays. Stability analysis and robust control of timedelay systems focuses on essential aspects of this field, including the stability analysis, stabilization, control design, and filtering of various timedelay systems. Stability analysis and control of discretetime systems.
Simple stability conditions of linear discrete time systems with multiple delay 71 2 model description and preliminaries a linear, autonomous, multivariable discrete timedelay system can be represented. To date, most work in this area has focused on sliding mode control 16, 17, 18 or on formulating conditions such that the system is stable for any switching rule. In 26, the robust stability, robust stabilization and. Robust stability of switched delay systems with average. Stability results for switched linear systems with constant. Delays exist universally in engineering systems, such as manufacturing processes, networked control systems, teleoperation of robots, remote surgery, multirobot systems, internal combustion engines, traffic dynamics, etc.
Knopse, and panagiotis tsiotras abstract it is demonstrated that many previously reported lyapunovbased stability conditions for timedelay systems are equivalent to the ro. The research presented in this thesis considers the stability analysis and control of discrete time systems with delay. Piecewise lyapunovrazumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of an infinite number of switchings. New results on stability of discretetime systems with. Recently, there has been considerable research on switched impulsive systems with time delay.
Since many of the applications of switching systems involve control, it is. Finitetime control for switched linear systems with. In this paper, a simple switching signal design scheme for h. Narges tahmasbi et al control and stability of the timedelay linear systems296 jic email for contribution. The research presented in this thesis considers the stability analysis and control of discretetime systems with delay. In this paper, we intend to use the timeswitched method and the comparison. Stability of a class of linear switching systems with time delay.
Box 644, 48080 bilbao, spain 2 department of telecommunication and systems engineering. Stability of timedelay systems control engineering. Although the last decade has witnessed significant advances in control theory for finite and infinite dimensional systems, the stability and control of timedelay. Up to now, most of existing literature related to stability of switched systems investigates. Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of instability or oscillation. There are two kinds of stability for switched systems with time delay. Control of unstable and integrating time delay systems. The last section provides some illustrative examples. Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of. Introduction a variety of stability and control techniques have been developed for general time delay systems 2, 14, 16. On positive forms and the stability of linear timedelay. A switched system may be obtained from a hybrid system by.
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