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

Date
2013
Advisor
Instructor
Source Title
Systems and Control Letters
Print ISSN
0167-6911
Electronic ISSN
Publisher
Elsevier
Volume
62
Issue
6
Pages
511 - 516
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

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.

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Other identifiers
Book Title
Keywords
H∞ control, Infinite dimensional systems, Robust stabilization, Strong stabilization, Infinite-dimensional system, Linear time-invariant, Lower and upper bounds, Nevanlinna-Pick interpolation, Repetitive control system, Robust stabilization, Single input single output, Strong stabilization, Control system analysis, Interpolation, Poles, Robustness (control systems), Stabilization
Citation
Published Version (Please cite this version)