Switching regulation based stabilisation of discrete‐time 2D switched systems with stable and unstable modes

Abstract

This study investigates the stabilisation problem for a class of discrete-time two-dimensional (2D) switched systems. Here the 2D systems mean that the state evolves following two independent directions, which are usually represented as horizontal states and vertical states. The considered systems are represented by Roesser model and incorporate both stable and unstable modes. Based on a switching signal regulation approach, which restricted the switching number as well as the running time ratio between the unstable and stable modes, the exponential stability condition is established for the 2D switched systems with synchronous switching. Besides, solving the proposed stabilisation results in linear matrix inequality form, the stabilising controller gains can be obtained. Moreover, considering the time delay in the controllers when the switching occurs, the proposed results are extended to the stabilisation problem for the 2D switched systems under asynchronous switching. A numerical example further demonstrates the validity of the developed results.