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Robust controllability and observability degrees of polynomially uncertain systems


Robust controllability and observability degrees of polynomially uncertain systems

Sojoudi, Somayeh, Lavaei, Javad and Aghdam, Amir G. (2009) Robust controllability and observability degrees of polynomially uncertain systems. Automatica, 45 (11). pp. 2640-2645. ISSN 00051098

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Aghdam2009d.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1016/j.automatica.2009.07.017


This paper deals with the class of polynomially uncertain continuous-time linear time-invariant (LTI) systems whose uncertainties belong to a semi-algebraic set. The objective is to determine the minimum of the smallest singular value of the controllability or observability Gramian over the uncertainty region. This provides a quantitative measure for the robust controllability or observability degree of the system. To this end, it is shown that the problem can be recast as a sum-of-squares (SOS) problem. In the special case when the uncertainty region is polytopic, the corresponding SOS formulation can be simplified significantly. One can apply the proposed method to any large-scale interconnected system in order to identify those inputs and outputs that are more effective in controlling the system, in a robust manner. This enables the designer to simplify the control structure by ignoring those inputs and outputs whose contribution to the overall control operation is relatively weak. A numerical example is presented to demonstrate the efficacy of the results.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Authors:Sojoudi, Somayeh and Lavaei, Javad and Aghdam, Amir G.
Journal or Publication:Automatica
Digital Object Identifier (DOI):10.1016/j.automatica.2009.07.017
Keywords:Analysis of systems with uncertainties; Optimization under uncertainties; Sum-of-squares; Large scale systems
ID Code:975171
Deposited On:22 Jan 2013 14:16
Last Modified:18 Jan 2018 17:39


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