Observer-based finite-time control for discrete fuzzy jump nonlinear systems with time delays

This paper investigates the problem of observer-based finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a family of discrete 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stabilization via observer-based fuzzy state feedback are provided for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. A simulation example is presented to illustrate the validity of our contributions.