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

Fu-Peng Li, Rui-Hua Wang*, and Shu-Min Fei
International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp.1142-1153, 2022

Abstract : 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 (TDCC) 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.

Keyword : Discrete-time switched systems, slow/fast admissible edge-dependent average dwell time, transferringdependent convex controller, transferring-dependent convex Lyapunov function.

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