Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays.

This article analyzes the singular switched positive systems with time-varying distributed delays from the perspective of positivity, exponential stability and disturbance attenuation performance referring to both L1-gain and L∞-gain. For the system, a sufficient and necessary positivity condition is firstly developed by using the singular value decomposition technique. Then, a sufficient condition of exponential stability, which makes the considered system exponentially stable, is proposed on the basis of co-positive Lyapunov–Krasovskii functional and average dwell time techniques, and the obtained exponential decay rate can be adjusted in the light of various actual situations. Furthermore, the article analyzes the disturbance attenuation performance referring to both L1-gain and L∞-gain, and through the convex optimization approach, the optimal L1-gain and L∞-gain performance level could be established, respectively. Three examples are finally presented to show the feasibility and effectiveness of the obtained results.