Author:
Younus Awais,Atta Gulnaz,Aloqaily Ahmad,Mlaiki Nabil,Abdeljawad Thabet
Abstract
AbstractLinear dynamic systems with impulsive effects are considered. For such a system we define a new impulsive exponential matrix. Necessary and sufficient conditions for exponential stability and boundedness have been established. The fundamental tool is an impulsive exponential matrix for exponential stability.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference27 articles.
1. Lakshmikantham, V., Simeonov, P.S., et al.: Theory of Impulsive Differential Equations, vol. 6. World Scientific, New Jersey (1989)
2. Milman, V.D., Myshkis, A.D.: On the stability of motion in the presence of impulses. Sib. Mat. Zh. 1(2), 233–237 (1960)
3. Wang, Y., Lu, J.: Some recent results of analysis and control for impulsive systems. Commun. Nonlinear Sci. Numer. Simul. 80, 104862 (2020)
4. Lupulescu, V., Younus, A.: On controllability and observability for a class of linear impulsive dynamic systems on time scales. Math. Comput. Model. 54(5–6), 1300–1310 (2011)
5. Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18(1–2), 18–56 (1990)