A Razumikhin approach for the incremental stability of delayed nonlinear systems

Antoine Chaillet 1, * Alexander Pogromsky 2 Björn Rüffer 3
* Corresponding author
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
3 Signal and System Theory Group
University of Paderborn
Abstract : This paper provides sufficient conditions for the incremental stability of time-delayed nonlinear systems. It relies on the Razumikhin-Lyapunov approach, which consists in invoking small-gain arguments by treating the delayed state as a feedback perturbation. The results are valid for multiple delays, as well as bounded time-varying delays. We provide conditions under which the limit solution of a time-delayed nonlinear system in response to a periodic (resp. constant) input is itself periodic and of the same period (resp. constant). As an illustration, a specific focus is given on a class of delayed Lur'e systems.
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Antoine Chaillet, Alexander Pogromsky, Björn Rüffer. A Razumikhin approach for the incremental stability of delayed nonlinear systems. 52nd IEEE Conference on Decision and Control CDC 2013, Dec 2013, Florence, Italy. pp.1-8, ⟨10.1109/cdc.2013.6760110 ⟩. ⟨hal-00855656⟩

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