Abstract
In this article, we elaborated on the problem of fixed time stability (FxTS) of nonlinear impulsive systems. For handing this problem, we propose a new concept of fixed-time stable function set (FTSFS). By taking advantage of definitions of FTSFS and average impulsive interval, a unified FxTS criterion of nonlinear impulsive systems is presented, which is applicable to both destabilising impulses and stabilising impulses. Comparing with the available work, the proposed Lyapunov function is allowed to possess indefinite derivatives when deriving from the state trajectory of nonlinear impulsive systems. Finally, two numerical examples are provided to support the proposed criterion.
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