Robust controllability and observability degrees of polynomially uncertain systems

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• 作者：Somayeh Sojoudi ; Javad Lavaei ; Amir G. Aghdam
• 关键词：Analysis of systems with uncertainties ; Optimization under uncertainties ; Sum-of-squares ; Large scale systems
• 刊名：Automatica
• 出版年：2009
• 出版时间：November 2009
• 年：2009
• 卷：45
• 期：11
• 页码：2640-2645
• 全文大小：2965 K

文摘

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.