Stable controllers for robust stabilization of systems with infinitely many unstable poles

This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that t...

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Bibliographic Details
Published in:Systems & control letters 2013-06, Vol.62 (6), p.511-516
Main Authors: Wakaiki, Masashi, Yamamoto, Yutaka, Özbay, Hitay
Format: Article
Language:English
Subjects:
[formula omitted] control
Control systems
Controllers
Infinite dimensional systems
Interpolation
Perturbation methods
Poles
Repetitive control
Robust stabilization
Stability
Strong stabilization
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Summary:This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation–minimization by a unit element. Next, by the modified Nevanlinna–Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2013.02.005