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arXiv · 1905.12397

Passive discrete-time systems with a Pontryagin state space

Lassi Lilleberg
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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.

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Lassi Lilleberg. 2019-05-29. Passive discrete-time systems with a Pontryagin state space. https://arxiv.org/abs/1905.12397

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