A descriptor system approach to H ∞ control of linear time-delay systems

E. Fridman; Uri Shaked

doi:10.1109/9.983353

A descriptor system approach to H _∞ control of linear time-delay systems

E. Fridman^*, Uri Shaked

^*Corresponding author for this work

School of Electrical Engineering

IEEE

Research output: Contribution to journal › Article › peer-review

839 Scopus citations

Abstract

The output-feedback H _∞ control problem is solved for continuous-time, linear, retarded and neutral type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Park's inequality for bounding cross terms. A state-feedback solution is derived for systems with polytopic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay "innovation filter." The cases of instantaneous and delayed measurements are considered. Numerical examples are given which illustrate the effectiveness of the new theory.

Original language	English
Pages (from-to)	253-270
Number of pages	18
Journal	IEEE Transactions on Automatic Control
Volume	47
Issue number	2
DOIs	https://doi.org/10.1109/9.983353
State	Published - Feb 2002

Funding

Funders	Funder number
Ministry of Absorption of Israel
Tel Aviv University

Keywords

Delay-dependent criteria
Descriptor systems
H -control
Linear matrix inequalities (LMIs)
Time-delay systems

Access to Document

10.1109/9.983353

Cite this

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abstract = "The output-feedback H ∞ control problem is solved for continuous-time, linear, retarded and neutral type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Park's inequality for bounding cross terms. A state-feedback solution is derived for systems with polytopic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay {"}innovation filter.{"} The cases of instantaneous and delayed measurements are considered. Numerical examples are given which illustrate the effectiveness of the new theory.",

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note = "Funding Information: Manuscript received November 6, 2000; revised November 27, 2000 and July 10, 2001. Recommended by Associate Editor Y. Yamamoto. This work was supported by the Ministry of Absorption of Israel, and by the C and M Maus Chair at Tel Aviv University. The authors are with the Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: [email protected]). Publisher Item Identifier S 0018-9286(02)02064-0.",

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