Asynchronous L1 control of delayed switched positive systems with mode-dependent average dwell time

This paper investigates the stability and asynchronous L1 control problems for a class of switched positive linear systems (SPLSs) with time-varying delays by using the mode-dependent average dwell time (MDADT) approach. By allowing the co-positive type Lyapunov–Krasovskii functional to increase during the running time of active subsystems, a new stability criterion for the underlying system with MDADT is first derived. Then, the obtained results are extended to study the issue of asynchronous L1 control, where “asynchronous” means that the switching of the controllers has a lag with respect to that of system modes. Sufficient conditions are provided to guarantee that the resulting closed-loop system is exponentially stable and has an L1-gain performance. Finally, two numerical examples are given to show the effectiveness of the developed results.