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LMI-based robust control of uncertain discrete-time piecewise affine systems
Received:2008/5/23  Revised:2009/1/13
Keywords:Discrete-time systems  Linear matrix inequality  Piecewise affine systems  Piecewise Lyapunov function  Robust control
Fund Project:This work was supported by the National Science Fund of China for Distinguished Young Scholars (No.60725311).
AuthorInstitutionE-mail
Zhiyuan LIU Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China  
Yahui GAO Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China hitgyh@163.com 
Hong CHEN Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China  
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Abstract:
      The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine (PWA) systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively. The basic idea of the proposed approaches is to construct piecewise-quadratic (PWQ) Lyapunov functions to guarantee the stability of the closed-loop systems. The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid, then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities (LMIs). Two examples are given to illustrate the proposed theoretical results.
Zhiyuan LIU,Yahui GAO and Hong CHEN.LMI-based robust control of uncertain discrete-time piecewise affine systems[J].Journal of Control Theory and Applications,2010,8(4):496~502.
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