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On state-space energy based generalization of Brayton–Moser topological approach to electrical network decomposition

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Abstract

This paper deals with generalization of the Brayton–Moser network decomposition and related structural properties to a relatively large class of finite dimensional strictly causal systems, which can be described in the state-space representation form. The resulting energy-metric function is defined for dissipative systems and is induced by the output signal dissipation power. It is demonstrated that such a power-oriented approach determines both, the structure of a system representation as well as the corresponding system state space topology. A special form of physically correct internal structure of an equivalent state space representation has been derived as a natural consequence of strict causality, the state-space energy conservation, dissipativity assumption and the state minimality requirement.

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Abbreviations

SSE:

State space energy

TSE:

Total system energy

BM:

Brayton–Moser

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Acknowledgments

This research was supported by the European Regional Development Fund and Ministry of Education, Youth and Sports of the Czech Republic under project No. CZ.1.05/2.1.00/03.0094: Regional Innovation Centre for Electrical Engineering (RICE). M. Stork is with the Regional Innovation Centre for Electrical Engineering, University of West Bohemia, Univerzitni 22, Plzen, Czech Republic.

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Authors and Affiliations

  1. Department of Theory of Electrical Engineering, University of West Bohemia/RICE, Plzen, Czech Republic

    Daniel Mayer

  2. Department of Applied Electronics and Telecommunications, University of West Bohemia/RICE, Plzen, Czech Republic

    Josef Hrusak & Milan Stork

Authors
  1. Daniel Mayer
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  2. Josef Hrusak
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  3. Milan Stork
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Correspondence to Milan Stork.

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Mayer, D., Hrusak, J. & Stork, M. On state-space energy based generalization of Brayton–Moser topological approach to electrical network decomposition. Computing 95 (Suppl 1), 723–749 (2013). https://doi.org/10.1007/s00607-012-0280-2

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  • DOI: https://doi.org/10.1007/s00607-012-0280-2

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