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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Official URL: http://dx.doi.org/10.1016/j.automatica.2009.07.017
Abstract
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 |
| Refereed: | Yes |
| Authors: | Sojoudi, Somayeh and Lavaei, Javad and Aghdam, Amir G. |
| Journal or Publication: | Automatica |
| Date: | 2009 |
| 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 By: | Danielle Dennie |
| Deposited On: | 22 Jan 2013 14:16 |
| Last Modified: | 18 Jan 2018 17:39 |
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