Finite-time input-to-state stability of time-varying stochastic hybrid time-delay systems

This work is concerned with the finite-time input-to-state stability (FTISS) for impulsive switched stochastic time-delay systems. Two cased of hybrid systems are investigated: (i) the impulsive instants and switching instants are synchronous; (ii) the impulsive instants and switching instants are asynchronous. Furthermore, we allow the upper bound of Lyapunov-Razumikhin function with two indefinite derivatives. Then, by using the technique of Lyapunov-Razumikhin, comparison principles combined with the mode-dependent average dwell time (MDADT) and the mode-dependent average impulsive interval (MDAII), we obtain the FTISS property. Finally, we give an example to apply our result and verify its effectiveness.