Lyapunov regularity and stability of linear non-instantaneous impulsive differential systems

In this paper, we discuss Lyapunov regularity and stability for linear non-instantaneous impulsive differential systems. In particular, we give sufficient conditions to guarantee any non-trivial solution has a finite Lyapunov exponent and we prove an impulsive system is stable using the Lyapunov exp...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 84; no. 4; pp. 712 - 747
Main Authors Wang, JinRong, Li, Mengmeng, O’Regan, Donal
Format Journal Article
LanguageEnglish
Published 01.08.2019
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Summary:In this paper, we discuss Lyapunov regularity and stability for linear non-instantaneous impulsive differential systems. In particular, we give sufficient conditions to guarantee any non-trivial solution has a finite Lyapunov exponent and we prove an impulsive system is stable using the Lyapunov exponent for the solution. A new version of Perron’s theorem is given by introducing the associated adjoint impulsive system and some criteria for the existence of non-uniform exponential behaviour are given. In addition, we present a stability result for a small perturbed nonlinear impulsive system when the linear impulsive system admits a non-uniform exponential contraction. Finally, we give a bound for the regularity coefficient.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxz012