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On stability for generalized linear differential equations and applications to impulsive systems
Published online by Cambridge University Press: 15 February 2023
Abstract
In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterization of them in terms of upper bounds and asymptotic behaviour of the transition matrix. In addition, we illustrate our stability results for GLDEs to linear periodic systems and linear impulsive differential equations. Finally, we prove that the well-known definitions of uniform asymptotic stability and variational asymptotic stability are equivalent to the global uniform exponential stability introduced in this article.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 2 , April 2024 , pp. 381 - 407
- Copyright
- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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