Stability and Controller Design of Discrete-time Switched Systems Based on Transferring-dependent Lyapunov Function Approach

This paper studies stability and controller design for discrete-time switched systems with unstable subsystems under the slow/fast admissible edge-dependent average dwell time (AED-ADT) switching. Different from the previous research results, it is the first time to propose transferring-dependent convex Lyapunov function (CLF) and transferring-dependent Lyapunov function (LF). Then, considering a slow/fast AED-ADT switching scheme, some excellent stability criteria are established according to transferring-dependent CLF and transferring-dependent LF, which have less restrictiveness compared with existing results. Corresponding to the novel transferring-dependent LFs and the properties of slow/fast AED-ADT switching, the new transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC) are devised to stabilize the underlying system. Finally, the effectiveness of the proposed approach is verified by two numerical examples.