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

This paper investigates the problem of robust H ∞ 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 ∞ 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 ∞ 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.