Stability, l1-gain and l∞-gain analysis for discrete-time positive switched singular delayed systems

In this paper, the problems of stability, l1-gain and l∞-gain analysis for positive switched singular systems with time delay are addressed. Both l1-gain and l∞-gain performance are analyzed. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by introducing new state vectors, the positive switched singular system is transformed into a standard positive switched system, and sufficient conditions for the positive switched singular delayed system to be asymptotically stable with an l1-gain performance and an l∞-gain performance are obtained, respectively. Finally, three numerical examples are presented to demonstrate the proposed results.