Abstract
This article investigates the fixed-time stability (FXTS) of discontinuous impulsive systems. Based on the generalized Lyapunov functional (LF) method and some inequality techniques, we propose some novel FXTS criteria of the systems. It is worth mentioning that the derivative of LF can be negative definite or indefinite, and these results extend the previous results significantly. Furthermore, by using the monotonicity of the integral functions and the existence theorem of zero points, we obtain the FXTS results under the influence of impulses. In particular, when taking some certain functions, we can easily estimate the settling-time. Finally, the main results are confirmed by numerical simulations.
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