Delay-Derivative/Distribution Dependent Stability and Stabilization Criteria for T–S Fuzzy Systems With Random Time-Varying Delay
Zongming Yin, Xiefu Jiang
Abstract
This article is concerned with the problems of stability and stabilization for Takagi–Sugeno (T–S) fuzzy systems with random time-varying delay. Since the stochastic nature of delay is considered, the original systems are transformed into equivalent new system models. Then, by borrowing the constant delay decomposition method, an appropriate Lyapunov–Krasovskii (L–K) functional is constructed. Based on the L–K functional, the variation range, the probabilities in intervals, and the derivative of delay can be effectively utilized. And the reciprocally convex inequality is used to estimate the upper bound of the integral terms from the derivative of L–K functional. The new delay-derivative/distribution-dependent stability and stabilization criteria are derived. Different from the previous works, the information of delay derivative is effectively utilized to analyze and design the systems with random time-varying delay for the first time. Moreover, if delay is a known time-varying function, less conservative stability and stabilization conditions can be obtained by the proposed delay decomposition method. Finally, the merits of the obtained stability and stabilization criteria are illustrated via several examples.