On the Stability of Cyclic or Periodically Switched Systems Under Unstable Switching Sub-Modes

In this brief, emphasis is placed on the global uniform asymptotic stability analysis of a switched system formulated by cyclic or periodic switching laws. First, several concepts and properties of cyclic or periodically switched systems are defined. Next, by using the cycle dwell time or cyclic period time switching method, new stability criteria for cyclic or periodically switched systems with all Hurwitz stable sub-systems are obtained in the context of general solutions. Moreover, new stability conditions for cyclic or periodically switched systems with partially unstable sub-modes are derived in the framework of general solutions. Finally, two examples are provided to demonstrate the feasibility of the developed criteria.