Improved input-to-state stability criteria for time-varying switched singular systems

This paper is dedicated to proposing improved input-to-state stability (ISS) criteria for a class of continuous-time time-varying switched singular systems (CTSSS) under slow/fast/slow-fast switching signals. Specifically, for a CTSSS with time-varying singular matrices, the authors start with an improved sufficient condition for verifying its ISS under slow switching signals based on the average dwell time method and a relaxed multiple Lyapunov function. Then, considering several or all subsystems may destroy the overall ISS, relaxed sufficient conditions are presented to ensure the ISS of the CTSSS under fast switching signals and slow-fast switching signals, respectively. Note that the improvement of the proposed ISS criteria is embodied in the derivative of the required multiple Lyapunov functions along with the state trajectories of CTSSS can be positive or negative. Finally, three numerical examples are provided to illustrate the feasibility of the obtained results.