Frequency-domain robust performance condition for controller uncertainty in SISO LTI systems: a geometric approach

Authors:
Vahid Raissi Dehkordi;Benoit Boulet
Affiliations:
Department of Electrical and Computer Engineering, Centre for Intelligent Machines, McGill University, Montréal, QC, Canada;Department of Electrical and Computer Engineering, Centre for Intelligent Machines, McGill University, Montréal, QC, Canada
Venue:
Journal of Control Science and Engineering
Year:
2009

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Abstract

This paper deals with the robust performance problem of a linear time-invariant control systemin the presence of robust controller uncertainty. Assuming that plant uncertainty ismodeled 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 themagnitude 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.