Finite-time H∞ control for discrete-time switched nonlinear systems with time delay

In this paper, the problem of finite-time H∞ control is addressed for a class of discrete-time switched nonlinear systems with time delay. The concept of H∞ finite-time boundedness is first introduced for discrete-time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay-dependent sufficient conditions are derived to guarantee the H∞ finite-time boundedness of the closed-loop system. Then, a finite-time H∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite-time H∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water-quality control system are provided to demonstrate the effectiveness of the main results.