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

Keqin Gu; Yashun Zhang; Matthew Peet

doi:10.1007/978-3-642-25221-1_3

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

Keqin Gu, Yashun Zhang, Matthew Peet

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Time Delay Systems
Subtitle of host publication	Methods, Applications and New Trends
Editors	Rifat Sipahi, Tomas Vyhlidal, Silviu-Iulian Niculescu, Pierdomenico Pepe
Pages	35-47
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-642-25221-1_3
State	Published - 2012
Externally published	Yes

Publication series

Name	Lecture Notes in Control and Information Sciences
Volume	423
ISSN (Print)	0170-8643

ASJC Scopus subject areas

Library and Information Sciences

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10.1007/978-3-642-25221-1_3

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Positivity of complete quadratic Lyapunov-Krasovskii functionals in time-delay systems. / Gu, Keqin; Zhang, Yashun; Peet, Matthew.
Time Delay Systems: Methods, Applications and New Trends. ed. / Rifat Sipahi; Tomas Vyhlidal; Silviu-Iulian Niculescu; Pierdomenico Pepe. 2012. p. 35-47 (Lecture Notes in Control and Information Sciences; Vol. 423).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - 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.

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ER -

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

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