Improved results on stability and stabilization of T-S fuzzy systems with random time-varying delay

This article explores the stability and stabilization (SAS) problems of T-S fuzzy systems with random time-varying delay (RTVD). To begin with, an augmented delay-product-type Lyapunov-Krasovskii functional (LKF) is constructed. Such an LKF has not been applied to the analysis and design of the systems with RTVD in previous studies, due to the obstacle caused by the coupling between the system delay function and the defined delay functions. Next, the generalized free-matrix-based integral inequality (GFMBII) is employed to bound the integral terms, and the augmented state variables technique is adopted to prevent the emergence of nonlinear expressions related to the defined delay functions. Moreover, with the aid of the constructed LKF, some RTVD dependent free matrices are effectively introduced. Then, by appropriately handling the coupling relationship between the system delay function and the defined delay functions, new SAS criteria are obtained, which are tractable and significantly less conservative. Finally, two examples are presented to demonstrate the advantages of the proposed criteria.