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Measures for controllability, observability and fixed modes

机译:可控制性,可观察性和固定模式的措施

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摘要

Measures are introduced that provide quantitative information about relative controllability and observability of a linear multivariable system. The proposed measures are directly related to frequency-domain characteristics such as zeros and residues, and to time-domain characteristics such as eigenvectors, controllability and observability Gramians and eigenvalue sensitivity. A simple and computationally efficient formula involving a quadratic form in the input (output) matrix and the left (right) eigenvector is presented for the calculation of controllability (observability) measure. For systems with repeated eigenvalues, the measures are shown to be proportional to the distances of transmission zeros of certain subsystems and the eigenvalues. The results are extended to decentralized systems, where a measure for fixed modes is proposed.
机译:引入了提供关于线性多变量系统的相对可控性和可观察性的定量信息的措施。所提出的措施与频域特征(例如零和残差)以及时域特征(例如特征向量,可控制性和可观察性革兰氏度和特征值敏感性)直接相关。提出了一个简单且计算有效的公式,该公式在输入(输出)矩阵和左(右)特征向量中包含二次形式,用于计算可控制性(可观察性)度量。对于具有重复特征值的系统,测度显示为与某些子系统的透射零距离和特征值成比例。结果扩展到分散系统,其中提出了针对固定模式的措施。

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