Asynchronous Control and Stabilization of Linear Switched Systems with Unstabilizable Subsystems by Average Dwell Time Approach

Stabilization of switched linear systems is one of the most important problems in the field of switched systems. On the other hand, asynchronous switching between the controller and the system may lead to an unstable closed loop system or degrade the closed loop system's performance. In this paper the problem of stabilizing a switched system with both stabilizable and unstabilizable subsystems and asynchronous switching between the controller and the system is considered. Using Lyapunov-like functions, some criteria are presented to guarantee the stability of the switched system based on the activity time of the stable and unstable subsystems and maximum number of switchings in a given time interval for both discrete-time and continuous-time cases. The last issue, verified in this paper is the design of a state feedback controller which can provide stability criteria, as well as designer’s desired criteria, including minimum activity time of the stable subsystems. In order to illustrate the effectiveness of the proposed method, simulation results are presented at the end of the paper.