Continuous approximation of linear impulsive systems and a new form of robust stability
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Date
2018-01-01
Authors
Church, Kevin E. M.
Smith, Robert J.
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive system can be affected by replacing the impulse effect with a continuous (as opposed to discontinuous, impulsive) perturbation, producing what is known as an impulse extension equation. Theoretical properties related to the existence of the time-scale tolerance are given for periodic systems, as are algorithms to compute them. Some methods are presented for general, aperiodic systems. Additionally, sufficient conditions for the convergence of solutions of impulse extension equations to the solutions of their associated impulsive differential equation are proven. Counterexamples are provided.
Description
The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.jmaa.2017.08.026 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
Exponential regulator, Impulse extension, Impulsive differential equations, Robust stability, Stability, Time-scale tolerance