Stability and L1-Gain Analysis for Switched Time-Delay Positive Systems With Persistent Dwell Time Switching

In this article, the stability and
$L$
1
-gain performance analysis of switched time-delay positive systems (STDPSs) is explored. The more general persistent dwell time (PDT) switching is used to investigate STDPSs for the first time. Then, a co-positive type Lyapunov-Krasovskii functional (CPTLKF) is constructed. The stability conditions of the STDPSs are established based on the CPTLKF and PDT. Furthermore, based on the stability analysis results, the unweighted L
1
-gain for STDPSs is explored, which has explicit physical meaning compared with the weighted results. The upper bound of the unweighted L
1
-gain can be obtained by a linear programming (LP) problem. Compared with the results obtained by dwell time (DT) or average dwell time (ADT), the results obtained by PDT in this article are less conservative. An example verifies the effectiveness of the proposed methods.