## Abstract

Passive systems t = {T, M, N, H} with M and N as an input and output space and H as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established. A passive system t with M = N is said to be quasi-selfadjoint if ran (T - T*). N. The subclass S(qs)(N) of the Schur class S(N) is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass S(qs)(N) is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function belonging to the subclass S(qs) (N) and the Q-function of T is given.

Original language | English |
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Pages (from-to) | 19-56 |

Number of pages | 38 |

Journal | Complex analysis and operator theory |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar-2009 |

## Keywords

- Passive system
- transfer function
- quasi-selfadjoint contraction
- Q-function
- DISCRETE-TIME-SYSTEMS
- HERMITIAN CONTRACTIONS
- SCATTERING SYSTEMS
- EXTENSIONS
- MATRICES
- KREIN