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The pole placement theorem and small perturbations in parameters: the existence of an unassignable left half plane

机译:极点定理和参数中的小扰动:存在不可分配的左半平面

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摘要

It is proved that placing the poles of a linear time-invariant system arbitrarily far to the left of the imaginary axis is not possible if small perturbations in the model coefficients are taken into account. The results show a major difference between the behavior of nominal closed-loop system poles and the closed-loop system poles under small perturbations of the open-loop system parameters. For systems with uncertain parameters there exists an unassignable left half plane.
机译:事实证明,如果考虑模型系数的微小扰动,则不可能将线性时不变系统的极点任意放置在虚轴的左侧。结果表明,在较小的开环系统参数扰动下,标称闭环系统极点与闭环系统极点的行为之间存在很大差异。对于参数不确定的系统,存在不可分配的左半平面。

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