A LMI approach to stability of descriptor systems with delay

E. Fridman

doi:10.23919/ecc.2001.7076368

A LMI approach to stability of descriptor systems with delay

E. Fridman^*

^*Corresponding author for this work

School of Electrical Engineering

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

Abstract

The Lyapunov second method is developed for linear coupled system 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 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 lead to less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.

Original language	English
Title of host publication	2001 European Control Conference, ECC 2001
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2871-2876
Number of pages	6
ISBN (Electronic)	9783952417362
DOIs	https://doi.org/10.23919/ecc.2001.7076368
State	Published - 2001
Event	6th European Control Conference, ECC 2001 - Porto, Portugal Duration: 4 Sep 2001 → 7 Sep 2001

Publication series

Name	2001 European Control Conference, ECC 2001

Conference

Conference	6th European Control Conference, ECC 2001
Country/Territory	Portugal
City	Porto
Period	4/09/01 → 7/09/01

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10.23919/ecc.2001.7076368

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abstract = "The Lyapunov second method is developed for linear coupled system 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 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 lead to less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.",

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AB - The Lyapunov second method is developed for linear coupled system 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 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 lead to less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.

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PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 6th European Control Conference, ECC 2001

Y2 - 4 September 2001 through 7 September 2001

ER -

A LMI approach to stability of descriptor systems with delay

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