Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach

M.N.A. Parlakçι, I.B. Küçükdemiral

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate the design problem of a stabilizing control for a class of linear uncertain time-delay systems with time-varying state and input delays. The control law is selected to be a state-feedback controller. Adopting to employ an augmented type of Lyapunov-Krasovskii functional, for the nominal case, we first derive some sufficient delay-dependent stabilization criteria which can be solved using a convex optimization technique with interior-point algorithms. The stabilization synthesis is then extended to the case when the time-delay system is subject to the norm-bounded uncertainties which affect state and input matrices. Several numerical examples are presented to demonstrate the application of the proposed synthesis of a stabilizing controller. The numerical results on the maximum allowable delay bound and the uncertainty bound seem to be quite less conservative in comparison to the existing methods from the literature.
Original languageEnglish
Title of host publication9th IFAC Workshop on Time Delay Systems
EditorsTomas Vyhlidal, Pavel Zitek
PublisherElsevier B.V.
Pages212-217
Number of pages6
Volume43
Edition2
DOIs
Publication statusPublished - 2010

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Time delay
Stabilization
Controllers
Convex optimization
State feedback
Uncertainty

Keywords

  • input delay
  • state delay
  • norm-bounded uncertainties
  • stability
  • stabilisation

Cite this

Parlakçι, M. N. A., & Küçükdemiral, I. B. (2010). Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. In T. Vyhlidal, & P. Zitek (Eds.), 9th IFAC Workshop on Time Delay Systems (2 ed., Vol. 43, pp. 212-217). Elsevier B.V.. https://doi.org/10.3182/20100607-3-CZ-4010.00039
Parlakçι, M.N.A. ; Küçükdemiral, I.B. / Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. 9th IFAC Workshop on Time Delay Systems. editor / Tomas Vyhlidal ; Pavel Zitek. Vol. 43 2. ed. Elsevier B.V., 2010. pp. 212-217
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Parlakçι, MNA & Küçükdemiral, IB 2010, Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. in T Vyhlidal & P Zitek (eds), 9th IFAC Workshop on Time Delay Systems. 2 edn, vol. 43, Elsevier B.V., pp. 212-217. https://doi.org/10.3182/20100607-3-CZ-4010.00039

Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. / Parlakçι, M.N.A.; Küçükdemiral, I.B.

9th IFAC Workshop on Time Delay Systems. ed. / Tomas Vyhlidal; Pavel Zitek. Vol. 43 2. ed. Elsevier B.V., 2010. p. 212-217.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - In this paper, we investigate the design problem of a stabilizing control for a class of linear uncertain time-delay systems with time-varying state and input delays. The control law is selected to be a state-feedback controller. Adopting to employ an augmented type of Lyapunov-Krasovskii functional, for the nominal case, we first derive some sufficient delay-dependent stabilization criteria which can be solved using a convex optimization technique with interior-point algorithms. The stabilization synthesis is then extended to the case when the time-delay system is subject to the norm-bounded uncertainties which affect state and input matrices. Several numerical examples are presented to demonstrate the application of the proposed synthesis of a stabilizing controller. The numerical results on the maximum allowable delay bound and the uncertainty bound seem to be quite less conservative in comparison to the existing methods from the literature.

AB - In this paper, we investigate the design problem of a stabilizing control for a class of linear uncertain time-delay systems with time-varying state and input delays. The control law is selected to be a state-feedback controller. Adopting to employ an augmented type of Lyapunov-Krasovskii functional, for the nominal case, we first derive some sufficient delay-dependent stabilization criteria which can be solved using a convex optimization technique with interior-point algorithms. The stabilization synthesis is then extended to the case when the time-delay system is subject to the norm-bounded uncertainties which affect state and input matrices. Several numerical examples are presented to demonstrate the application of the proposed synthesis of a stabilizing controller. The numerical results on the maximum allowable delay bound and the uncertainty bound seem to be quite less conservative in comparison to the existing methods from the literature.

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Parlakçι MNA, Küçükdemiral IB. Robust delay-dependent stabilizing control of time-delay systems with state and input delays: augmented L.K. functional approach. In Vyhlidal T, Zitek P, editors, 9th IFAC Workshop on Time Delay Systems. 2 ed. Vol. 43. Elsevier B.V. 2010. p. 212-217 https://doi.org/10.3182/20100607-3-CZ-4010.00039