Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters

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• 作者：Jun-Wei Wang^a ; ^{wangjunwei1984@yahoo.com.cn} ; ^{wangjunwei-1984@163.com}  ; [Author Vitae] ; Huai-Ning Wu^a ; ¹ ; ^{whn@buaa.edu.cn} ; ^{huainingwu@163.com}  ; [Author Vitae] ; Han-Xiong Li^b ; ^{mehxli@cityu.edu.hk}  ; [Author Vitae]
• 关键词：Distributed parameter systems ; Markov jumping parameters ; Stochastically exponential stability ; Robust control ; Linear matrix inequalities (LMIs)
• 刊名：Automatica
• 出版年：2012
• 期刊代码：13_00051098
• 类别：cp
• 出版时间：March, 2012
• 卷：48
• 期：3
• 页码：569-576
• 文件大小：548 K

摘要

This paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first-order hyperbolic partial differential equations (FOHPDEs) with Markov jumping parameters, for which the manipulated input is distributed in space. Based on an integral-type stochastic Lyapunov functional (ISLF), the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities (SDLMIs). Then, an SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition. Furthermore, using the finite difference method and the standard linear matrix inequality (LMI) optimization techniques, recursive LMI algorithms for solving the SDLMIs in the analysis and synthesis are provided. Finally, a simulation example is given to demonstrate the effectiveness of the developed design method.