Positivity of complete quadratic Lyapunov-Krasovskii functionals in time-delay systems

Keqin Gu, Yashun Zhang, Matthew Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This chapter discusses positivity of quadratic functionals that arise in the stability analysis of time-delay systems. When both the single and double integral terms are positive, a necessary and sufficient condition for positivity is obtained using operator theory. This is applied to the Lyapunov-Krasovskii functional and its derivative. The coupled differential-difference equations are studied using the Sum-of-Squares (SOS) method.

Original languageEnglish (US)
Title of host publicationTime Delay Systems
Subtitle of host publicationMethods, Applications and New Trends
EditorsRifat Sipahi, Tomas Vyhlidal, Silviu-Iulian Niculescu, Pierdomenico Pepe
Pages35-47
Number of pages13
DOIs
StatePublished - May 21 2012
Externally publishedYes

Publication series

NameLecture Notes in Control and Information Sciences
Volume423
ISSN (Print)0170-8643

ASJC Scopus subject areas

  • Library and Information Sciences

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    Gu, K., Zhang, Y., & Peet, M. (2012). Positivity of complete quadratic Lyapunov-Krasovskii functionals in time-delay systems. In R. Sipahi, T. Vyhlidal, S-I. Niculescu, & P. Pepe (Eds.), Time Delay Systems: Methods, Applications and New Trends (pp. 35-47). (Lecture Notes in Control and Information Sciences; Vol. 423). https://doi.org/10.1007/978-3-642-25221-1_3