Standard L1 Stability for Singular Switched Positive Systems with Time-Varying Distributed Delay Under MDRDT Constraint

Abstract

This paper is concerned with the standard [Formula: see text] stability with respect to singular switched positive systems (SSPSs) with time-varying distributed delays (TVDDs) under mode-dependent ranged dwell time (MDRDT) constraint. Firstly, for SSPSs with TVDDs under MDRDT constraint, a sufficient condition of asymptotical stability is proposed. Next, to analyze disturbance attenuation performance, a sufficient condition of standard [Formula: see text] stability is presented for SSPSs with TVDDs under MDRDT constraint. Via convex optimization approach, the corresponding standard [Formula: see text]-gain performance optimum can be received. In addition, the standard [Formula: see text] stability issue is also extended to the SSPSs in nonsingular case, in delay-free case and in RDT constraint case, respectively. Finally, the validity is proved by giving three examples.