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Criteria on Contraction and Incremental Stability of Dynamical Systems with Time Delay
Version 1
: Received: 18 April 2023 / Approved: 20 April 2023 / Online: 20 April 2023 (07:10:26 CEST)
A peer-reviewed article of this Preprint also exists.
Lang, Y.; Lu, W. Criteria on Exponential Incremental Stability of Dynamical Systems with Time Delay. Mathematics 2023, 11, 2242. Lang, Y.; Lu, W. Criteria on Exponential Incremental Stability of Dynamical Systems with Time Delay. Mathematics 2023, 11, 2242.
Abstract
Incremental stability analysis for time-delay systems has attracted more and more attentions for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches criteria on v(t)-incremental stability, which is defined to demonstrate the convergence rate for incremental stability, for time-delay systems. Firstly, the sufficient conditions for v(t)-incremental stability for time-delay systems with continuous right-hands are studied, and several corollaries for specific cases are provided. As for time-delay systems with discontinuous right-hands, after expounding the relevant conditions for the existence and uniqueness of the Filippov solution, by using approximation methods, sufficient conditions for v(t)-incremental stability are obtained. The conclusions are applied to linear switched time-delay systems and Hopfield neural network system with composite right-hand afterwards.
Keywords
Time-delay System; v(t)-Incremental Stability; Discontinuous Right-hands; Filippov solutions
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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