Robust H∞ fuzzy control for uncertain nonlinear Markovian jump systems with time-varying delay

This paper investigates the problem of robust H-infinity fuzzy control for a class of uncertain nonlinear Markovian jump systems with time-varying delay. The class of systems under consideration is described by the Takagi-Sugeno fuzzy model. The goal of the paper is to design a mode-dependent fuzzy state-feedback controller such that the closed-loop system is stochastically stable with a prescribed H-infinity performance of disturbance attenuation for all admissible parameter uncertainties. In order to obtain a less conservative control design, a new stochastic Lyapunov-Krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals. Then, by employing this functional, a delay decomposition approach to the design of robust H-infinity fuzzy controllers is developed in terms of linear matrix inequalities. Finally, two examples are given to illustrate the merit and usability of the proposed design method. (C) 2012 Elsevier B.V. All rights reserved.