NDLI: The Problem of the Absolute Continuity for Liapunov-Krasovskii Functionals

Content Provider	IEEE Xplore Digital Library
Author	Pepe, P.
Copyright Year	2006
Description	Author affiliation: Dipt. di Ingegneria Elettrica e dell'Informazione, Universita degli Studi dell'Aquila, L'Aquila (Pepe, P.)
Abstract	The condition of non-positivity, almost everywhere, of the upper right-hand Dini derivative of a (simply) continuous function is not a sufficient condition for such function to be non-increasing. That condition is sufficient for the non-increasing property if the function is locally absolutely continuous. Therefore, if the time function obtained by the evaluation of a Liapunov-Krasovskii functional on the solution of a time-delay system is not locally absolutely continuous, but simply continuous, and its upper right-hand Dini derivative is almost everywhere non-positive, then the conclusion that such function is non-increasing cannot be drawn. And, as a consequence, related stability conclusions cannot be drawn. In this paper such problem is investigated for input-to-state stability concerns of time invariant time-delay systems forced by measurable locally essentially bounded inputs. It is shown that, if the Liapunov-Krasovskii functional is locally Lipschitz with respect to the norm of the uniform topology, then the problem of the absolute continuity is overcome
Starting Page	4218
Ending Page	4223
File Size	194781
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377197
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability USA Councils Force measurement Time measurement Topology Delay effects Delay systems Nonlinear equations Time varying systems Liapunov-Krasovskii Theorem Input-to-State Stability (ISS) Functional Differential Equations Nonlinear Time-Delay Systems
Content Type	Text
Resource Type	Article

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