Finite-Time Stability and Instability of Nonlinear Impulsive Systems

IF 1.5 4区 工程技术 Q2 MATHEMATICS, APPLIED
Guihua Zhao null, Hui Liang
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引用次数: 2

Abstract

. In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems con-sidered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illus-trate the theoretical analysis.
非线性脉冲系统的有限时间稳定性和不稳定性
. 研究了非线性脉冲系统的有限时间稳定性和不稳定性。主要有四个问题。1)对于具有稳定脉冲的系统,给出了全局有限时间稳定性的Lyapunov定理。2)当无脉冲效应的系统是全局有限时间稳定系统(GFTS),并且在原点处的稳定时间是连续的,证明了在任意一类脉冲序列上,如果混合脉冲跳变满足一些温和的条件,该系统仍然是全局有限时间稳定系统。3)对于具有不稳定脉冲的系统,为了保证系统的有限时间稳定,不稳定脉冲的出现频率不能太高,否则,脉冲系统的原点是有限时间不稳定的,分别用平均停留时间(ADT)条件来表示。4)给出了具有稳定脉冲的系统的有限时间不稳定性定理。对于本文所考虑的脉冲系统的每一个GFTS定理,给出了稳定时间的上界,该上界取决于初始值和脉冲效应。给出了一些数值算例来说明理论分析。
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来源期刊
Advances in Applied Mathematics and Mechanics
Advances in Applied Mathematics and Mechanics MATHEMATICS, APPLIED-MECHANICS
CiteScore
2.60
自引率
7.10%
发文量
65
审稿时长
6 months
期刊介绍: Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.
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