A Fastly and Slowly Cyclic Switching Strategy for Discrete-Time Cyclic Switched Systems and Its Application to Inverter Circuits

In this brief, a fastly and slowly cyclic switching approach is designed for the stability of a class of discrete-time cyclic switched systems with unstable modes. Firstly, by developing two discrete-time cyclic switching laws (i.e., the so-called fastly unstable (or slowly stable) cycle-dependent average cycle dwell time), several new stability criteria for discrete-time cyclic switched nonlinear systems with unstable subsystems are derived in the form of multiple Lyapunov functions. Next, some stability conditions for discrete-time cyclic switched linear systems with unstable modes are also obtained in the case of linear matrix inequalities. It is worth noting that the obtained results provide tighter upper and lower limits for the running time of the system. Furthermore, a stability corollary for discrete-time cyclic switched nonlinear (linear) systems with all stable subsystems is presented. Finally, simulation results of a numerical example and a switching inverter circuit are given to illustrate the potential and efficiency of the developed techniques.