# Passive systems with a normal main operator and quasi-selfadjoint systems - Mathematics > Functional Analysis

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Abstract: Passive systems $\tau={T,M,N,H}$ with $M$ and $N$ as an input and outputspace and $H$ as a state space are considered in the case that the mainoperator on the state space is normal. Basic properties are given and a generalunitary similarity result involving some spectral theoretic conditions on themain operator is established. A passive system $\tau$ with $M=N$ is said to bequasi-selfadjoint if $ranT-T^*\subset N$. The subclass $S^{qs}$ of the Schurclass $S$ is the class formed by all transfer functions of quasi-selfadjointpassive systems. The subclass $S^{qs}$ is characterized and minimal passivequasi-selfadjoint realizations are studied. The connection between the transferfunction belonging to the subclass $S^{qs}$ and the $Q$-function of $T$ isgiven.

Autor: Yu.M. Arlinskiĭ, S. Hassi, H.S.V. de Snoo

Fuente: https://arxiv.org/