Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings

In this paper, the problems of stability analysis and stabilization are investigated for discrete-time two-dimensional (2-D) switched systems, which are formulated by the well-known Fornasini-Marchesini local state-space model. Firstly, by using the switched quadratic Lyapunov function approach, a sufficient stability condition is established for such systems under arbitrary switching signal. Then, the extended average dwell time technique combining with the piecewise Lyapunov function approach is developed, and it is utilized for the stability analysis of the 2-D switched systems for the restricted switching case. Based on the stability analysis results, sufficient conditions are presented to stabilize the 2-D switched systems. Finally, two examples are provided to illustrate the effectiveness of the proposed new design techniques.