Stabilization of switched positive linear delay system with all subsystems unstable

Abstract This article considers the asymptotic stability of switched positive linear time‐delay system with all subsystems unstable. By constructing new discretized co‐positive Lyapunov‐Krasovskii functions, stability conditions are derived for both the discrete time‐varying delay and distributed time‐varying delay cases. Then the results are also extended to nonpositive switched delay systems. Finally we apply our results to consensus problems of switched multi‐agent systems with time delay. We propose numerical examples to illustrate our approach.