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Journal of Control Science and Engineering
Volume 2009, Article ID 746762, 9 pages
Research Article

Frequency-Domain Robust Performance Condition for Controller Uncertainty in SISO LTI Systems: A Geometric Approach

Department of Electrical and Computer Engineering, Centre for Intelligent Machines, McGill University, 633-3480 University Street, Montréal, QC, H3A 2A7, Canada

Received 3 September 2008; Accepted 3 April 2009

Academic Editor: Andrea Garulli

Copyright © 2009 Vahid Raissi Dehkordi and Benoit Boulet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the robust performance problem of a linear time-invariant control system in the presence of robust controller uncertainty. Assuming that plant uncertainty is modeled as an additive perturbation, a geometrical approach is followed in order to find a necessary and sufficient condition for robust performance in the form of a bound on the magnitude of controller uncertainty. This frequency domain bound is derived by converting the problem into an optimization problem, whose solution is shown to be more time-efficient than a conventional structured singular value calculation. The bound on controller uncertainty can be used in controller order reduction and implementation problems.