Journal Article

Robust stabilization of linear systems with time-varying point delays via a delay-free dynamic controller

M. De la Sen

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 4, pages 395-413
Published in print December 2005 | ISSN: 0265-0754
Published online December 2005 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni026
Robust stabilization of linear systems with time-varying point delays via a delay-free dynamic controller

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This paper deals with the problem of robust closed-loop stabilization against parametrical uncertainties of linear systems subject to internal (i.e. in the state) and external (i.e. in the output), possibly time-varying and unbounded point delays of a bounded time-derivative. The output-feedback linear stabilizing controller is delay free and dynamic. It is assumed that the undelayed plant (i.e. the delay-free part of the plant) is stabilizable and detectable. The synthesis process of the stabilizing controller involves three major actions. First, an augmented system is built with the dynamic equations of both plant and controller. At this step, the controller structure is available but a particular stabilizing controller parametrization still remains undetermined. Subsequently, a Lyapunov matrix equation is ensured to be solvable for the augmented closed-loop delay-free system so that such a system is stable with a large stability abscissa related to the amounts of uncertainties and delay contributions to the dynamics. At this stage, one takes the advantage that the augmented system may be stabilized by an appropriate dynamic controller of minimum order since the undelayed plant is stabilizable and detectable. Finally, a complementary matrix equality is manipulated to establish the closed-loop stability tolerance of the augmented delay system, related to that of the delay-free one, to the delayed dynamics and parametrical uncertainties.

Keywords: Lyapunov matrix equation; Riccati matrix equation; robust stabilization; time-delay systems

Journal Article.  0 words. 

Subjects: Mathematics

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