H∞ finite time control for discrete time-varying system with interval time-varying delay

Abstract

This paper discusses the problem of H∞ finite time control for a discrete time-varying system with interval time-varying delay. By constructing a new augmented time-varying Lyapunov functional involving triple summation items and using discrete Wirtinger-type inequalities, delay-dependent conditions are derived, which guarantee that the closed-loop system is not only finite time bounded (FTB) but also satisfies an H∞ performance. Furthermore, the time-varying feedback controller can be derived by solving a series of recursive linear matrix inequalities (RLMIs). Simulation results show the effectiveness and superiority of the proposed method.