Robust finite-time fuzzy H_∞ control for uncertain time-delay systems with stochastic jumps

摘要

This paper investigates the problem of robust finite-time H_∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi-Sugeno (T-S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H_∞ stabilization are presented. Then, by using stochastic Lyapunov-Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H_∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H_∞ stabilization using a fuzzy state-feedback controller are provided, and the controller is designed by solving an optimization problem in terms of linear matrix inequalities. Finally, two numerical examples are exploited to show the validity of the proposed design techniques.