Robust delay-dependent H-infinity control of time-delay systems with state and input delays

M.N. Alpaslan Parlakci, Ibrahim B. Kucukdemiral

Research output: Contribution to journalArticle

Abstract

This paper studies the design problem of robust delay dependent H infinity controller for a class of time delay control systems with time varying state and input delays, which are assumed to be noncoincident. The system is subject to norm bounded uncertainties and L2 disturbances. Based on the selection of an augmented form of Lyapunov Krasovskii (LK) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay dependent criteria are developed for a stabilizing H infinity controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm bounded uncertainties, both the BRL and H infinity stabilization criteria are easily extended by employing a well known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature.
Original languageEnglish
Pages (from-to)974-1007
Number of pages34
JournalInternational Journal of Robust and Nonlinear Control
Volume21
Issue number9
Publication statusPublished - Jun 2011

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Linear matrix inequalities
Time delay
Delay control systems
Controllers
Stabilization
Uncertainty

Keywords

  • H infinitive control
  • state delay
  • input delay
  • norm-bounded uncertainties
  • linear matrix inequalities

Cite this

Parlakci, M. N. A., & Kucukdemiral, I. B. (2011). Robust delay-dependent H-infinity control of time-delay systems with state and input delays. International Journal of Robust and Nonlinear Control, 21(9), 974-1007.
Parlakci, M.N. Alpaslan ; Kucukdemiral, Ibrahim B. / Robust delay-dependent H-infinity control of time-delay systems with state and input delays. In: International Journal of Robust and Nonlinear Control. 2011 ; Vol. 21, No. 9. pp. 974-1007.
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Parlakci, MNA & Kucukdemiral, IB 2011, 'Robust delay-dependent H-infinity control of time-delay systems with state and input delays', International Journal of Robust and Nonlinear Control, vol. 21, no. 9, pp. 974-1007.

Robust delay-dependent H-infinity control of time-delay systems with state and input delays. / Parlakci, M.N. Alpaslan; Kucukdemiral, Ibrahim B.

In: International Journal of Robust and Nonlinear Control, Vol. 21, No. 9, 06.2011, p. 974-1007.

Research output: Contribution to journalArticle

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AB - This paper studies the design problem of robust delay dependent H infinity controller for a class of time delay control systems with time varying state and input delays, which are assumed to be noncoincident. The system is subject to norm bounded uncertainties and L2 disturbances. Based on the selection of an augmented form of Lyapunov Krasovskii (LK) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay dependent criteria are developed for a stabilizing H infinity controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm bounded uncertainties, both the BRL and H infinity stabilization criteria are easily extended by employing a well known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature.

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Parlakci MNA, Kucukdemiral IB. Robust delay-dependent H-infinity control of time-delay systems with state and input delays. International Journal of Robust and Nonlinear Control. 2011 Jun;21(9):974-1007.