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Robust controllability and observability degrees of polynomially uncertain systems. (English) Zbl 1180.93020

Summary: 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.

MSC:

93B05 Controllability
93B07 Observability
93B35 Sensitivity (robustness)
93C41 Control/observation systems with incomplete information

Software:

YALMIP; Matlab; Sostools
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Full Text: DOI Link

References:

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