Observer-based H∞ control of uncertain singular systems with time-varying delay

Lin Li; Yingmin Jia; Junping Du; Shiying Yuan

doi:10.1109/WCICA.2008.4593392

Observer-based H_∞ control of uncertain singular systems with time-varying delay

Lin Li^*
, Yingmin Jia
, Junping Du
, Shiying Yuan

^*Corresponding author for this work

School of Automation Science and Electrical Engineering

Beihang University
Beijing University of Posts and Telecommunications
Henan Polytechnic University

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

4 Scopus citations

Abstract

This paper is devoted to the problem of robust H_∞ control for a class of uncertain singular systems with time-varying delay and norm-bounded parameter uncertainties. The states of the singular system are unmeasured. A state feedback controller based on an observer is proposed. The observer system is singular and with the same dimension as that of the given singular system. By employing free-weighting matrix and linear matrix inequality (LMI) approach, a new stability criterion for the nominal and unforced singular system is obtained. Based on this criterion, a delay-dependent sufficient condition is given to ensure that there exists an observer-based state feedback stabilizing controller such that the augmented closed-loop system is regular, impulse free and stable with the prescribed H_∞ performance level for all admissible parameter uncertainties, and the corresponding design algorithm of observer and controller is proposed. A numerical example is included to show the effectiveness of the proposed method.

Original language	English
Title of host publication	Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007
Pages	2940-2945
Number of pages	6
DOIs	https://doi.org/10.1109/WCICA.2008.4593392
State	Published - 2008
Event	7th World Congress on Intelligent Control and Automation, WCICA'08 - Chongqing, China Duration: 25 Jun 2008 → 27 Jun 2008

Publication series

Name	Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

Conference

Conference	7th World Congress on Intelligent Control and Automation, WCICA'08
Country/Territory	China
City	Chongqing
Period	25/06/08 → 27/06/08

Keywords

Delay-dependent
H control
LMI
Observer
Singular systems

Access to Document

10.1109/WCICA.2008.4593392

Cite this

Li, L., Jia, Y., Du, J., & Yuan, S. (2008). Observer-based H_∞ control of uncertain singular systems with time-varying delay. In Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007 (pp. 2940-2945). Article 4593392 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA)). https://doi.org/10.1109/WCICA.2008.4593392

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title = "Observer-based H∞ control of uncertain singular systems with time-varying delay",

abstract = "This paper is devoted to the problem of robust H∞ control for a class of uncertain singular systems with time-varying delay and norm-bounded parameter uncertainties. The states of the singular system are unmeasured. A state feedback controller based on an observer is proposed. The observer system is singular and with the same dimension as that of the given singular system. By employing free-weighting matrix and linear matrix inequality (LMI) approach, a new stability criterion for the nominal and unforced singular system is obtained. Based on this criterion, a delay-dependent sufficient condition is given to ensure that there exists an observer-based state feedback stabilizing controller such that the augmented closed-loop system is regular, impulse free and stable with the prescribed H∞ performance level for all admissible parameter uncertainties, and the corresponding design algorithm of observer and controller is proposed. A numerical example is included to show the effectiveness of the proposed method.",

keywords = "Delay-dependent, H control, LMI, Observer, Singular systems",

author = "Lin Li and Yingmin Jia and Junping Du and Shiying Yuan",

year = "2008",

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language = "英语",

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booktitle = "Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007",

note = "7th World Congress on Intelligent Control and Automation, WCICA'08 ; Conference date: 25-06-2008 Through 27-06-2008",

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Li, L, Jia, Y, Du, J & Yuan, S 2008, Observer-based H_∞ control of uncertain singular systems with time-varying delay. in Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007., 4593392, Proceedings of the World Congress on Intelligent Control and Automation (WCICA), pp. 2940-2945, 7th World Congress on Intelligent Control and Automation, WCICA'08, Chongqing, China, 25/06/08. https://doi.org/10.1109/WCICA.2008.4593392

Observer-based H_∞ control of uncertain singular systems with time-varying delay. / Li, Lin; Jia, Yingmin; Du, Junping et al.
Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007. 2008. p. 2940-2945 4593392 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA)).

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

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N2 - This paper is devoted to the problem of robust H∞ control for a class of uncertain singular systems with time-varying delay and norm-bounded parameter uncertainties. The states of the singular system are unmeasured. A state feedback controller based on an observer is proposed. The observer system is singular and with the same dimension as that of the given singular system. By employing free-weighting matrix and linear matrix inequality (LMI) approach, a new stability criterion for the nominal and unforced singular system is obtained. Based on this criterion, a delay-dependent sufficient condition is given to ensure that there exists an observer-based state feedback stabilizing controller such that the augmented closed-loop system is regular, impulse free and stable with the prescribed H∞ performance level for all admissible parameter uncertainties, and the corresponding design algorithm of observer and controller is proposed. A numerical example is included to show the effectiveness of the proposed method.

AB - This paper is devoted to the problem of robust H∞ control for a class of uncertain singular systems with time-varying delay and norm-bounded parameter uncertainties. The states of the singular system are unmeasured. A state feedback controller based on an observer is proposed. The observer system is singular and with the same dimension as that of the given singular system. By employing free-weighting matrix and linear matrix inequality (LMI) approach, a new stability criterion for the nominal and unforced singular system is obtained. Based on this criterion, a delay-dependent sufficient condition is given to ensure that there exists an observer-based state feedback stabilizing controller such that the augmented closed-loop system is regular, impulse free and stable with the prescribed H∞ performance level for all admissible parameter uncertainties, and the corresponding design algorithm of observer and controller is proposed. A numerical example is included to show the effectiveness of the proposed method.

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Li L, Jia Y, Du J, Yuan S. Observer-based H_∞ control of uncertain singular systems with time-varying delay. In Proceedings - CIS Workshops 2007, 2007 International Conference on Computational Intelligence and Security Workshops, CISW 2007. 2008. p. 2940-2945. 4593392. (Proceedings of the World Congress on Intelligent Control and Automation (WCICA)). doi: 10.1109/WCICA.2008.4593392