Delay-dependent stability analysis and synthesis of uncertain T--S fuzzy systems with time-varying delay

  • Authors:

  • Engang Tian;Chen Peng

  • Affiliations:

  • Department of Electrical Automation, Donghua University, No. 1882, Yan An West Road, Shanghai 200051, PR China;Center for Information & Control Engineering Technology, Nanjing Normal University, 78 Banchang Street, Nanjing, Jiangsu, PR China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

This paper considers the delay-dependent stability analysis and controller design for uncertain T-S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov-Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained. By constructing the Lyapunov-Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays. The efficiency of our method is demonstrated by two numerical examples.