Application of commutator calculus to the study of linear impulsive systems

被引：13

作者：

Slyn'ko, V. I. ^{[1
]}

Tunc, Osman ^{[2
]}

Bivziuk, V. O. ^{[3
]}

机构：

[1] SP Timoshenko Inst Mech NAS Ukraine, Stabil Proc Dept, Nesterov Str 3, UA-03680 Kiev 57, Ukraine

[2] Yuzuncu Yil Univ, Fac Sci, Dept Math, TR-65080 Van Turkey, Turkey

[3] Bohdan Khmelnytsky Natl Univ Cherkasy, Dept Algebra & Math Anal, Cherkassy, Ukraine

来源：

SYSTEMS & CONTROL LETTERS | 2019年 / 123卷

关键词：

Impulsive differential equation; Hybrid systems; Stability; Commutator calculus; Lyapunov's direct method; Lyapunov functions; Average dwell-time condition; STABILITY ANALYSIS; TIME; APPROXIMATION; STABILIZATION; CRITERIA; DESIGN;

D O I：

10.1016/j.sysconle.2018.10.015

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, the formulas of commutator calculus are applied to the investigation of the stability of linear impulsive differential equations. It is assumed that the moments of impulse action satisfy the average dwell-time (ADT) condition. Sufficient conditions for the asymptotic stability of linear impulsive differential equations in a Banach space are obtained. In the Hilbert space, the stability of the original linear differential equation is reduced to the investigation of a linear differential equation with equidistant moments of impulse action and perturbed discrete dynamics. This reduction simplifies the application of Lyapunov's direct method and the construction of Lyapunov functions. We give examples in the spaces R-2 and X = C[0, l] to illustrate the effectiveness of results obtained. Finally, a sufficient generality of the obtained results on the dynamic properties of linear operators of the linear impulsive differential equation is established. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：160 / 165

页数：6

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