Switching stabilization and l2-gain analysis for 2D discrete switched systems with time-varying delays

This paper addresses the exponential stability and l
₂
-gain analysis for a class of two-dimensional (2D) discrete switched systems with time-varying delays. The concept of mode-dependent average dwell time (MDADT) is extended to 2D switched systems with state delays. Then, based on the MDADT approach and Lyapunov-Krasovskii (LK) function approach, two sufficient conditions are derived to design switching signal and guarantee the exponential stability and l
₂
-gain for the considered 2D discrete switched systems, which are delay-dependent and formulated by linear matrix inequalities (LMIs), which can be effectively solved by resorting to some standard convex optimisation algorithms. Finally, a numerical example is provided to demonstrate the applicability of the proposed controller design approach.