Robust finite-time H∞H∞ control for uncertain discrete jump systems with time delay

This paper addresses the robust finite-time H∞H∞ control problem for a family of uncertain discrete-time Markovian jump systems with time delay. Initially, the concepts of stochastic finite-time boundedness and stochastic H∞H∞ finite-time stabilization are given. Then, a stochastic finite-time H∞H∞ controller is designed such that the underlying closed-loop discrete jump time-delay system is stochastic finite-time boundedness and satisfies a prescribed H∞H∞ performance level in some given finite-time interval. Based on Lyapunov approach, sufficient criteria on the stochastic H∞H∞ finite-time stabilization are established for the solvability of the problem, which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter. Finally, simulation examples are presented to demonstrate the validity of the developed techniques.