Exponential stability for positive singular systems without/with time-varying distributed delays

Abstract

This paper analyzes the problem of positivity and exponential stability for positive singular systems(PSSs) without/with time-varying distributed delays. Firstly, by using the singular value decomposition technique, a sufficient and necessary condition of positivity is firstly developed for the system without or with time-varying distributed delays, respectively. Then, based on the co-positive Lyapunov function approach, a sufficient condition of exponential stability is derived for the PSSs in delay-free case. Furthermore, considering the time-varying distributed delay case, a sufficient delay-dependent condition of exponential stability is derived for the PSSs via the co-positive Lyapunov-Krasovskii functional approach. The obtained exponential decay rate can be adjusted according to various actual situations. Two examples are finally presented to show the feasibility and effectiveness of the obtained results.