Finite-time stabilization for discrete fuzzy jump nonlinear systems with time delays

This paper is concerned with the problem of finite-time H _∞ control for a class of discrete-time Markovian jump nonlinear systems with time delays represented by Takagi-Sugeno (T-S) model. First, by using fuzzy stochastic Lyapunov-Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastic finite-time bounded and satisfies a prescribed H _∞ disturbance attenuation level in a given finite-time interval. Second, sufficient criteria on stochastic finite-time H _∞ stabilization via fuzzy state feedback are provided, and the fuzzy state feedback controller is designed by solving an optimization problem in terms of linear matrix inequalities. Finally, a numerical example is given to show the validity of the proposed designed techniques.