Delay-dependent robust H∞ control for uncertain discrete-time fuzzy systems with time-varying delays

  • Authors:
  • Baoyong Zhang;Shengyuan Xu

  • Affiliations:
  • School of Automation, Nanjing University of Science and Technology, Nanjing, China;School of Automation, Nanjing University of Science and Technology, Nanjing, China

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2009

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Abstract

This paper deals with the robust H∞ control problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parametric uncertainties and interval time-varying delays. First, based on a new Lyapunov functional, we present a sufficient condition guaranteeing that the resulting closed-loop system is robustly stable and satisfies a prescribed H∞ performance level. The Lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time-varying delay as well. Second, two classes of delay-dependent conditions for the existence of the concerned H∞ fuzzy controllers are given in terms of relaxed linear matrix inequalities (LMIs), and a desired controller can be designed by using the solutions to these LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.