Asynchronous L_1 control of delayed switched positive systems with mode-dependent average dwell time

摘要

This paper investigates the stability and asynchronous L_1 control problems for a class of switched positive linear systems (SPLSs) with time-varying delays by using the modedependent 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 L_1 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 L_1-gain performance. Finally, two numerical examples are given to show the effectiveness of the developed results.