Multi-rate sampled-data control for T-S fuzzy systems with mismatched fuzzy basis functions.

This paper investigates a multi-rate sampled-data (MRSD) stabilization criterion for T-S fuzzy systems with the consideration of mismatched fuzzy basis functions (FBFs). To fully exploit the system information under a MRSD mechanism, we incorporate an improved looped-functional and a discontinuous function into the Lyapunov-Krasovskii functional (LKF). This construction explicitly leverages the most recent measurements and the sampling-induced delay associated with each system state. Furthermore, to address a set of conditions expressed as parameterized linear matrix inequalities (PLMIs), this paper develops a refined relaxation technique for mismatched FBFs that explicitly exploit their inherent properties. Finally, two examples are provided to demonstrate the effectiveness and practicality of the proposed method.