Exponential Stability for Continue-Time Switched Positive Delay Systems with All Unstable Subsystems

In this paper, the stability of continue-time switched positive delay systems (SPDSs) with all unstable subsystems is investigated. Based on the time-scheduled multiple co-positive Lyapunov-Krasovskii functional (MCLKF) method combined with fast average dwell time (ADT) techniques, a sufficient condition is obtained to ensure the underlying system is exponentially stable. Compared with the results in existing literature, our work has two advantages. On the one hand, the proposed method is independent of the maximum of corresponding elements of each subsystem matrix, which overcomes the limitation of the existing method. On the other hand, our result is less conservative than that of the previous literature. In addition, the stability condition of the system in this paper is given by matrix inequality, which can be solved by nonlinear programming. Finally, two simulation examples are provided to illustrate the correctness and effectiveness of the main result.