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On l1 stability of switched positive singular systems with time‐varying delay

This paper investigates the problem of exponential stability and l1‐gain performance analysis for a class of discrete‐time switched positive singular systems with time‐varying delay. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by constructing an appropriate co‐positive Lyapunov functional and using the average dwell time scheme, we develop a sufficient delay‐dependent condition and identify a class of switching signals for the switched positive singular system to be exponentially stable and meet a prescribed l1‐gain performance level under the switching signal. Based on this condition, the decay rate of the system can be tuned and the optimal system performance level can be determined by solving a convex optimization problem. All of the criteria obtained in this paper are presented in terms of linear programming, which suggests a good scalability and applicability to high dimensional systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.