L∞-gain analysis for positive singular time-delay systems

This paper is devoted to the characterization of L∞-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the L∞-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the L∞-gain for singular system with time-varying delays. It is shown that the L∞-gain of positive singular systems is independent of the magnitude of delays.