Switching-Dependent Convex Lyapunov Function and Controller for Continuous-Time Switched Systems

In this paper, the stability and stabilization are investigated for continuous-time switched systems with admissible edge-dependent average dwell time (AED-ADT). The core idea is to propose new-type Lyapunov functions (LFs), i.e., switching-dependent convex Lyapunov function (CLF) and switching-dependent LF, to achieve the less conservative stability criteria. Corresponding to the novel LFs, two controller design approaches are built to stabilize the underlying system, which are switching-dependent convex controller under an innovative switching scheme and switching-dependent traditional controller under AED-ADT. In the end, a numerical example is provided to verify the effectiveness of the designed LFs in the aspect of stability analysis; a tunnel diode circuit is employed to unfold the potency of the above controller design approaches in optimizing control performances, such as settling time and overshoot.

Automated summary

This paper investigates the stability and stabilization of continuous-time switched systems with admissible edge-dependent average dwell time (AED-ADT). By proposing new-type Lyapunov functions and two controller design approaches, less conservative stability criteria and optimized control performances are achieved.