H∞ stabilization of 2-D discrete switched delayed systems represented by the Roesser model subject to actuator saturation

Abstract

This paper is concerned with the problem of state feedback H∞ stabilization for a class of 2-D (two-dimensional) discrete-time switched delayed systems with saturation on the control input. First, a sufficient condition for asymptotical stability and H∞ disturbance attenuation performance of the underlying system is derived using a new multiple Lyapunov functional. Second, the convex hull is used to describe the saturation behaviour and a sufficient condition for the existence of a state feedback controller, which ensures that the resulting closed-loop system is asymptotically stable and achieves a prescribed disturbance attenuation level, is developed in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed methodology.