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This note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Hankel singular values of a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis, that is, move from the left-(right-)half to the right-(left-)half of the...
This paper presents a new algorithm for realization of Gramian-preserving frequency transformation for linear discrete-time systems. In the proposed algorithm, we construct allpass systems for frequency transformation as the cascaded normalized lattice structure. It is shown that the frequency transformation based on this algorithm not only leaves the controllability/observability Gramians invariant...
This paper proposes a new expression of frequency transformation for linear continuous-time state-space systems. The proposed frequency transformation preserves the controllability Gramian and the observability Gramian of prototype state-space systems, and thus allows us to easily realize various kinds of state-space systems keeping the same realization as that of prototype state-space systems. Our...
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