Stabilization of Switched Logical Networks: Asynchronous Switching Control

This brief deliberates on the stabilization of switched logical networks (SLNs) under the asynchronous switching controller. The studied system takes into account the asynchronous switching phenomenon that the operating subsystem does not match the controller mode caused by non-ideal conditions. Our purpose is to find suitable conditions under which the SLN achieves stabilization under the asynchronous switching controller. By combining the Lyapunov method of logical networks and the mode-dependent average dwell time method, a sufficient criterion is first put forward for the stabilization of SLNs under the asynchronous switching controller. Furthermore, the obtained results are extended to the stabilization of SLNs with logical switching. An example of $lac$ operon in the $E.~coli$ is finally given to validate the addressed results.