Exponential Stability of Nonlinear Impulsive and Switched Time-Delay Systems with Delayed Impulse Effects

The exponential stability problem is considered for a class of nonlinear impulsive and switched time-delay systems with delayed impulse effects by using the method of multiple Lyapunov–Krasovskii functionals. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for stabilizing delayed impulses and destabilizing delayed impulses. It is shown that even if all the subsystems governing the continuous dynamics without impulse input delays are not exponential stable, if impulsive and switching signal satisfy a dwell-time upper bound condition, stabilizing delayed impulses can stabilize the systems in the exponential stability sense. Moreover, it is also shown that if the magnitude of the delayed impulses is sufficiently small, the exponential stability properties can be derived irrespective of the size of the impulse input delays under some conditions. The opposite situation is also developed. The efficiency of the proposed results is illustrated by two numerical examples.

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