Quasi-time-dependent stabilisation for 2-D switched systems with persistent dwell-time

This paper is concerned with the stabilisation problem for a class of discrete-time two-dimensional (2-D) switched systems with persistent dwell-time (PDT). The systems are described by the well-known Fornasini-Marchesini local state space (FMLSS) model. The concept of PDT switching signals is introduced herein, and each stage consists of a dwell-time period in which no switching occurs and a persistent period an arbitrary switching occurs. Based on a proper Lyapunov function suitable to the PDT switching, which is both quasi-time-dependent (QTD) and mode-dependent, the QTD state feedback controller is designed to ensure the closed-loop system is exponentially stable. Compared with time-independent criteria, new results are more general and flexible, and have less conservativeness. Finally, two examples are provided to show the effectiveness and potential of our proposed methods.