New Robust $H_{\infty}$ Performance Condition for Uncertain Discrete-Time Systems

  • Zhai, Guisheng (Department of Opto-Mechatronics, Wakayama University) ;
  • Lin, Hai (Department of Electrical Engineering, University of Notre Dame) ;
  • Kim, Young-Bok (Department of Control & Mechanical Engineering, Pukyong National University)
  • Published : 2003.10.22

Abstract

In this paper, we establish a new robust $H_{\infty}$ performance condition for uncertain discrete-time systems with convex polytopic uncertainties. We express the condition as a set of linear matrix inequalities (LMIs), which are used to check stability and $H_{\infty}$ disturbance attenuation level by a parameter-dependent Lyapunov matrix. We show that the new condition provides less conservative result than the existing ones which use single Lyapunov matrix. We also show that the robust $H_{\infty}$ state feedback design problem for such uncertain discrete-time systems can be easily dealt with using the approach. The key point in this paper is to propose a kind of decoupling between the Lyapunov matrix and the system matrices in the parameter-dependent matrix inequality by introducing one new matrix variable.

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