Design of H∞-control for fuzzy time-delay systems

In this paper the design problems of H∞ output feedback controllers for Takagi-Sugeno fuzzy time-delay systems are considered. We first introduce Takagi-Sugeno fuzzy time-delay systems and the H∞-performance (norm) for stable fuzzy time-delay systems. We consider systems with multiple time-delays in state. We give a sufficient condition for the norm being less than a given number. We then consider the H∞-problems with output feedback controllers. Both memoryless controller and controller with memory are considered. In the design of output feedback controllers, the selection of the premise variables in the If-Then rules is important. As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system. In the first two cases we give a design method of H∞-controllers and sufficient conditions which guarantee the required H∞-performance of the closed-loop system. In the last case we give an H∞-controller for an approximation of the original system. Two examples are given to illustrate the theory.