Stability and Stabilization Condition for T-S Fuzzy Systems with Time-Delay under Imperfect Premise Matching via an Integral Inequality

Abstract

This paper focuses on the stability and stabilization analysis for the T-S fuzzy systems with time-delay under imperfect premise matching, in which the number of fuzzy rules and membership functions employed for the fuzzy model and fuzzy controller are different. By introducing an augmented Lyapunov-Krasovskii function containing a triple-integral term, a less conservative membership-dependent stability condition is proposed via an integral inequality. Moreover, a new design approach under imperfect premise matching is developed in the paper. Four numerical examples are given to illustrate the advantages of our approaches. A practical benchmark problem namely continuous Stirred Tank Reactor (CSTR) is discussed in details in order to further verify their effectiveness.

Keywords

• T-S fuzzy systems
• Time-delay
• Integral inequality
• Lyapunov-Krasovskii function (LKF)
• Imperfect premise matching