Sampled-Data Control for T-S Fuzzy Systems Using Refined Looped Lyapunov Functional Approach

Abstract

This paper studies the sampled-data control problem for Takagi-Sugeno (T-S) fuzzy systems with variable sampling. To lessen the conservatism of stability criteria, we introduce a refined looped Lyapunov functional (LLF). These functionals incorporate additional information on split sampling intervals and delayed states. Moreover, sampling-dependent matrix functions are presented to relax the conservativeness of the developed LLFs. By resorting to the refined LLFs, new stability and stabilization criteria for T-S fuzzy systems incorporating an H∞ performance are established. To validate the established conditions, a nonlinear permanent magnet synchronous motor and the Lorenz system are used to demonstrate the reduced conservatism and the merits of the presented methods.

Keywords

• refined looped functional
• Takagi-Sugeno fuzzy model
• sampled-data control
• <i>H</i>_∞ performance