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On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition

Abstract : Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this paper is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.
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Contributor : Hugo Lhachemi <>
Submitted on : Monday, December 21, 2020 - 11:11:33 AM
Last modification on : Monday, January 4, 2021 - 10:46:31 AM

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Hugo Lhachemi, Robert Shorten. On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press, ⟨10.1109/TAC.2020.3047358⟩. ⟨hal-03084494⟩

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