Exponential stability analysis for singular switched positive systems under dwell-time constraints

Abstract

The article addresses the exponential stability analysis for singular switched positive systems(SSPSs) under dwell-time constraints which include mode-dependent minimum dwell time(MDMDT), mode-dependent constant dwell time(MDCDT) and mode-dependent ranged dwell time(MDRDT) constraints. For SSPSs in both delay-free case and time-varying delay case, a sufficient exponential stability condition is proposed with MDMDT, MDCDT and MDRDT constraints, respectively, and the exponential decay rate can be set as a free parameter based on diverse circumstances. To analyze the dwell-time stability, a novel discretized linear copositive Lyapunov function(DLCLF) approach is introduced in the article, and compared with the general copositive and homogeneous Lyapunov function approach, the main advantage of the DLCLF technique is itself affine dependence on conditions of system matrix, which will be extended and utilized to systems with uncertainties or/and time-varying parameters quite easily. Meanwhile, the proposed condition of exponential stability under MDMDT(or MDCDT or MDRDT) constraint will be degenerated into the one under minimum dwell time(or constant dwell time or ranged dwell time) constraint for some specific situations, which implies that the considered MDMDT(or MDCDT or MDRDT) case is more general and practical. Finally, the validity and significance of the results are illustrated by seven examples.