A novel fixed-time stability of nonlinear impulsive systems: a two-stage comparison principle method

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.

Keywords:

• Fixed-time stability
• nonlinear impulsive system
• fixed-time stable function set
• average impulsive interval
• improved Lyapunov function method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Natural Science Foundation of Hunan Province (No. 2020JJ4012), China Postdoctoral Science Foundation (No. 2018M632207), Scientific Research Key Project of Hunan Provincial Education Department (No. 20A268), Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (No. BM2017002) and Teaching Reform Project of Ordinary Colleges and Universities in Hunan Province (No. 844).