Stability of linear descriptor systems with delay: A Lyapunov-based approach

Emilia Fridman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Lyapunov second method is developed for linear coupled systems of delay differential and functional equations. By conventional approaches such equations may be reduced to the neutral systems and the known results for the latter may be exploited. In the present paper we introduce a new approach by constructing a Lyapunov-Krasovskii functional that corresponds directly to the descriptor form of the system. Moreover, by representing a neutral system in the descriptor form we obtain new stability criteria for neutral systems which are less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability and for robustness of stability with respect to small delays are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.

Original languageEnglish
Pages (from-to)24-44
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume273
Issue number1
DOIs
StatePublished - 1 Sep 2002

Funding

FundersFunder number
Ministry of Absorption of Israel

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