LMI-based robust control of uncertain discrete-time piecewise affine systems

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• 作者：Zhiyuan Liu ; Yahui Gao ; Hong Chen
• 关键词：Discrete ; time systems ; Linear matrix inequality ; Piecewise affine systems ; Piecewise Lyapunov function ; Robust control
• 刊名：Control Theory and Technology
• 出版年：2010
• 出版时间：November 2010
• 年：2010
• 卷：8
• 期：4
• 页码：496-502
• 全文大小：203 KB
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• 作者单位：Zhiyuan Liu (1)
  Yahui Gao (1)
  Hong Chen (2)
  
  1. Harbin Institute of Technology, Harbin Heilongjiang, 150001, China
  2. Department of Control Science and Engineering, Jilin University, Changchun Jilin, 130025, China
  
• 刊物类别：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Rob
• 刊物主题：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Robotics, Mechatronics;
• 出版者：South China University of Technology and Academy of Mathematics and Systems Science, CAS
• ISSN：2198-0942

文摘

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. Keywords Discrete-time systems Linear matrix inequality Piecewise affine systems Piecewise Lyapunov function Robust control