Finite-time H∞ control for a class of discrete-time linear system

In this paper, the concept of H_∞ control for discrete-time systems is extended over a finite-time interval, we discuss the finite-time control H_∞ problem for discrete-time linear system with time-varying norm-bounded exogenous disturbance, the main aim is to design a state feedback controller which guarantees that the closed-loop system is finite-time boundedness and reduces the effect of the disturbance input on the controlled output. In order to solve the problem, some sufficient conditions which can be reduced to feasibility problem involving LMIs are presented. Finally, a numerical example is given to demonstrate the efficiency of the proposed method.