連続時間線形システムにおける周波数感度と感度最小構造

概要

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This paper proposes sensitivity analysis and synthesis of minimum sensitivity structures in continuous time linear state-space systems. A sensitivity function called frequency sensitivity is defined using the partial derivatives of a given transfer function with respect to the elements of coefficient matrices. The frequency sensitivity shows a degree of degradation of the frequency response due to small perturbations of the elements of coefficient matrices. A frequency measure called frequency sensitivity norm is defined using the norm of the frequency sensitivity. It is represented by controllability and observability Gramians. The minimum sensitivity structures, that minimize the frequency sensitivity norm, are synthesized via equivalent transformations. The minimum sensitivity structures are equal to balanced realizations in the wide sense. A numerical example shows that a minimum sensitivity structure has much lower sensitivity than a controllability canonical realization.
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