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On Passive and Conservative State/Signal Systems

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An Erratum to this article was published on 03 June 2010

Abstract

This article is devoted to a study of continuous-time passive and conservative systems within the state/signal framework. The main idea of the state/signal approach is to not a priori distinguish between inputs and outputs, but rather to combine these two into a single external signal. The so-called node space is introduced as the product of two copies of the state space of the system and one copy of the space where the external signals of the system live. This node space is equipped with a sesquilinear product that makes it a Kreĭn space. A generating subspace is defined as a closed subspace of the node space, and the node space determines the trajectories of a state/signal system. One of the main results of this article is that a subspace of the node space generates a passive state/signal system if and only if it is a maximally nonnegative subspace of the node space and it satisfies a certain nondegeneracy condition. In this case the generating subspace can be interpreted as the graph of a scattering-passive input/state/output system node.

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Authors and Affiliations

  1. Department of Mathematics, Åbo Akademi University, Fänriksgatan 3B, 20500, Åbo, Finland

    Mikael Kurula

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  1. Mikael Kurula
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Correspondence to Mikael Kurula.

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This research was supported by the Academy of Finland, project number 201016 and the Finnish Graduate School in Mathematical Analysis and its Applications.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00020-010-1794-7

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Kurula, M. On Passive and Conservative State/Signal Systems. Integr. Equ. Oper. Theory 67, 377–424 (2010). https://doi.org/10.1007/s00020-010-1787-6

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