Design of \(H_{\infty}\)-control for fuzzy time-delay systems
Design problems of \(H_{\infty}\) output feedback controllers for Takagi-Sugeno (TS) fuzzy time-delay systems are considered. TS fuzzy time-delay systems and the \(H_{\infty}\) performance (norm) for stable fuzzy time-delay systems are intoduced. Systems with multiple time-delays in the state are considered. A sufficient condition for the norm being less than a given number is provided. Further, the \(H_{\infty}\)-problem with output feedback controllers is considered. Both memoryless controllers and controllers with memory are designed. In the design of output feedback controllers, the selection of the premise variables in the IF-THEN rules is important. For the premise variables, three cases are considered: (i) the premise variable is given and can be used in the controller design, (ii) the premise variable coincides with the output of the underlying system, (iii) the premise variable coincides with the state of the system which is unobservable. In the first two cases the author proposes a design method, based on the linear theory, of \(H_{\infty}\) controllers and sufficient conditions which guarantee the required \(H_{\infty}\) performance of the closed-loop systems. In the last case, an \(H_{\infty}\) controller for an approximation of the original system is given. Two examples are given to illustrate the applicability of the proposed methodology.
scientific article; zbMATH DE number 2153575
scientific article