Finsler-based Sampled-data Controller Design for Takagi-Sugeno Systems

Abstract

This paper investigates the sampled-data control of continuous-time Takagi-Sugeno (T-S) fuzzy systems. The closed-loop dynamics is rewritten as a T-S system with input time-varying delays. In this context, asynchronous membership functions appears in the closed-loop dynamics. Thus, to reduce the conservatism of design conditions involving mismatch membership functions, a dedicated relaxation scheme is proposed. Then, from a convenient Lyapunov-Krasovskii function and the application of the Finsler’s Lemma, new LMI-based conditions are proposed for the design of sampled-data Parallel-Distributed-Compensation (PDC) controllers. An example is provided to illustrate the effectiveness of the proposed design methodology in simulation, as well as to highlight their conservatism improvement regarding to previous related results from the literature.