H∞ control design for discrete-time switched fuzzy systems

This paper investigates the H∞H∞ control design and asynchronous stabilization problems for a class of discrete-time switched Takagi and Sugeno (T–S) fuzzy systems. The studied fuzzy systems have two level functions, namely, crisp switching functions and local fuzzy weighting functions, which inherently contain the features of switched hybrid systems and T–S fuzzy systems. In addition, the considered switching instants have asynchronous phenomena between the system switching modes and the controller switching modes. Based on the theory of the switching Lyapunov stability and average-dwell time method, both the matched H∞H∞ state feedback controllers and the unmatched state feedback controllers are designed. Moreover, the global uniformly asymptotically stability (GUAS) conditions are proposed and formulated in the form of linear matrix inequalities (LMIs). An illustrated numerical example is provided to show the effectiveness of the obtained theoretical results.