Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation
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Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation Junjie Zhao · Jing Wang · Hao Shen
Received: 31 December 2011 / Revised: 27 January 2013 © Springer Science+Business Media New York 2013
Abstract This paper deals with the problem of robust stabilization for Markovian jump delayed systems with partially known transition rates subject to input saturation. The problem we address is the design of dynamic anti-windup compensators, which guarantee that the resulting closed-loop constrained systems are robustly mean-square stable. By employing local sector conditions and an appropriate Lyapunov-Krasovskii function, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method. Keywords Markovian jump delayed systems · Input saturation · Dynamic anti-windup · Partially known transition rates · Robust control 1 Introduction Recently, lots of significant researches focused on the design of dynamic anti-windup compensator for the systems with input saturation. In many practical systems, saturation causes the nonlinearity which may lead to performance degradation. In the past decades, a great number of results have been reported in [2, 3, 12, 13, 18, 19, 42, 43]. For instance, by using passivity theorem to deal with input saturation, some J. Zhao School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China e-mail: [email protected] J. Wang · H. Shen () School of Electrical Engineering and Information, Anhui University of Technology, Ma’anshan 243002, China e-mail: [email protected] J. Wang e-mail: [email protected]
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analysis results were presented in [12]. An optimization-based approach was proposed to design feedback and anti-windup gains of a controller subject to saturation in [3]. The static anti-windup synthesis problem for a class of linear systems with actuator amplitude and rate saturation was considered in [18]. The method based on multiobjective convex optimization was used to deal with the problem of anti-windup controller synthesis in [19]. By employing dynamic anti-windup scheme, the stability analysis and control synthesis problems for linear system with saturation were studied in [42, 43]. In addition, time delays which may cause difficulty in stability analysis and controller design are often encountered in many practical systems, and the stabilization problem of time-delay systems has attracted many researchers; see, e.g., [1, 5–7, 11, 15, 16, 29, 36–38], and the references therein. More recently, for time-delay systems with input saturation, the robust stabilization and optimal control problems were investigated in [27, 28]. On the other hand, considerable attention has been devoted to the study of Markovian jump systems in [9, 10, 20, 23–25, 30, 34, 41]. When taking time delays into account Markovian jump systems, various results on stability analysis [
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