SOS methods for stability analysis of neutral differential Ssystems

Matthew M. Peet, Catherine Bonnet, Hitay Özbay

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

Abstract

This paper gives a description of how "sum-of-squares" (SOS) techniques can be used to check frequency-domain conditions for the stability of neutral differential systems. For delay-dependent stability, we adapt an approach of Zhang et al. [10] and show how the associated conditions can be expressed as the infeasibility of certain semialgebraic sets. For delay-independent stability, we propose an alternative method of reducing the problem to infeasibility of certain semialgebraic sets. Then, using Positivstellensatz results from semi-algebraic geometry, we convert these infeasibility conditions to feasibility problems using sum-of-squares variables. By bounding the degree of the variables and using the Matlab toolbox SOSTOOLS [7], these conditions can be checked using semidefinite programming.

Original languageEnglish (US)
Title of host publicationTopics in Time Delay Systems
Subtitle of host publicationAnalysis, Algorithms and Contr
EditorsJean Jacques Loiseau, Wim Michiels, Silviu-Iulian Niculescu, Rifat Sipahi
Pages97-107
Number of pages11
DOIs
StatePublished - Oct 19 2009
Externally publishedYes

Publication series

NameLecture Notes in Control and Information Sciences
Volume388
ISSN (Print)0170-8643

ASJC Scopus subject areas

  • Library and Information Sciences

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  • Cite this

    Peet, M. M., Bonnet, C., & Özbay, H. (2009). SOS methods for stability analysis of neutral differential Ssystems. In J. J. Loiseau, W. Michiels, S-I. Niculescu, & R. Sipahi (Eds.), Topics in Time Delay Systems: Analysis, Algorithms and Contr (pp. 97-107). (Lecture Notes in Control and Information Sciences; Vol. 388). https://doi.org/10.1007/978-3-642-02897-7_9