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Robust controllability and observability degrees of polynomially uncertain systems

机译：多项式不确定系统的鲁棒可控性和可观测性

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This paper deals with the class of polynomially uncertain continuous-time linear time-invariant (LT1) 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.
机译：本文研究了不确定性属于半代数集的多项式不确定连续时间线性时不变（LT1）系统。目的是确定不确定性区域上的可控制性或可观性革兰氏最小奇异值中的最小值。这为系统的鲁棒可控性或可观察性程度提供了一种定量措施。为此，已表明该问题可以作为平方和（SOS）问题进行重铸。在特殊情况下，当不确定区域为多位题时，可以显着简化相应的SOS公式。可以将所提出的方法应用于任何大型互连系统，以便以健壮的方式识别在控制系统方面更有效的那些输入和输出。这使设计人员可以通过忽略对整体控制操作的贡献相对较弱的那些输入和输出来简化控制结构。数值例子说明了结果的有效性。

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