Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays

This paper is concerned with the problem of observer-based finite-time H ∞ control for a family of discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. The main contribution of this paper is to design an observer-based finite-time H ∞ controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H ∞ stabilization via observer-based fuzzy state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. Numerical examples are given to illustrate the validity of the proposed design approaches.