Year: 2019
Type: preprint
Abstract: Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative index of the state space is given. In this case, an isometric (co-isometric) system has a product representation corresponding to the left (right) Krein-Langer factorization of the transfer function. A new criterion, based on the inclusion of reproducing kernel spaces, when a product of two isometric (co-isometric) systems preserves controllability (observability), is obtained. The concept of the defect function is expanded for generalized Schur functions, and realizations of generalized Schur functions with zero defect functions are studied.
Source: arXiv (Cornell University)
Author: Lilleberg, Lassi
Institution: University of Vaasa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952742773