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On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition
- Source :
- IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Journal :
- IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press
- Publication Type :
- Report
- Accession number :
- edsarx.2012.14665
- Document Type :
- Working Paper