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This paper studies integral input-to-state stability (iISS) of a class of hybrid delayed systems with impulse and switching behavior, in which the delay-dependent impulse and switching behavior are allowed for asynchronous occurrence. Relative to admissible edge-dependent average dwell time (AED-ADT) concept of the switching signal, a fresh concept of admissible edge-dependent average impulsive interval (AED-AII) is proposed for the impulse signal. Several sufficient criteria for iISS are achieved by using multiple Lyapunov–Krasovskii functional (MLKF) tool, AED-ADT switching, and AED-AII schemes. An improved inequality that describing the relation among Lyapunov function continuous switching signal and discrete impulse is constructed, where the jump amplitude at discrete switching points and impulsive moments including delay-dependent part and delay-independent part are involved. Compared with existing results, our conclusions have the following novelties: (1) the influence of time delay existing in continuous dynamics and discrete impulse on the function part of L-K functional is dug out, which is less conservative; (2) the AED-AII scheme proposed in this paper is combined with the AED-ADT switching method, which contains a larger set of the impulsive and switching signal. Moreover, the stability criterion is suitable for the arbitrary time delay in situation that all the subsystems are destabilizing. Finally, an example is given to verify the validity of the results. [ABSTRACT FROM AUTHOR]

This article focuses on a class of nonlinear random impulsive and switched systems for stochastic input-to-state stability. The impulse is divided into two types: single jump map and multiple jump maps. When the impulse is chosen as single jump map, it means that the impulse between the two adjacent switching times is single as well as impulse and switching occur simultaneously, in which the impulsive moments are fixed. When the impulse is chosen as multiple jump maps, in this model, the impulse is not only limited by multiple maps, but also the impulse instants are assumed to be random. Therefore, this model is an extension of the traditional impulsive and switched system. In view of admissible edge-dependent average dwell time switching signal and the impulse dynamic satisfying Poisson's process, sufficient conditions for the stochastic input-to-state stability are introduced into nonlinear impulsive switched system with random impulses. Three significant distinctions from the existing results rest with that (1) a new multiple Lyapunov functions are first created; the novelty contains discontinuity at the discrete points including switching moments and the impulse jump instants of Lyapunov-like functional; (2) the coefficient of derivative of a Lyapunov-like functions is permitted to be either positive or negative, which is less conservative; (3) the adopted admissible edge-dependent average dwell time switching scheme delves into less conservative stochastic input-to-state stability condition than mode-dependent average dwell time switching, nonlinear impulsive switched system with various jump maps. Numerical examples are simulated to manifest the validity of the main results. [ABSTRACT FROM AUTHOR]