Stability analysis for stochastic time‐delayed systems allowing admissible edge‐dependent switching signals

Abstract

This article extends stochastic input‐to‐state stability (SISS$$ \mathrm{SISS} $$) to stochastic time‐delayed hybrid systems with the properties of edge dependent. By quoting multiple Lyapunov–Krasovskii functional, comparison principle in association with admissible edge‐dependent average dwell time (AED‐ADT$$ \mathrm{AED}\hbox{-} \mathrm{ADT} $$) approach and admissible amputated edge‐dependent average impulsive interval (AAED‐AII$$ \mathrm{AAED}\hbox{-} \mathrm{AII} $$) technology, several novel stability criteria of hybrid time‐delayed stochastic systems are established. We allow impulsive jump and subsystem switching to occur at different instants. Furthermore, a new method named AAED‐AII is recommended for gap between impulses, which is an improvement for mode‐dependent average impulsive interval. Finally, a practical example is given to show the effectiveness of the new design techniques.