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Interconnection of [formula omitted]-lossless behaviours

Authors
Journal
Systems & Control Letters
0167-6911
Publisher
Elsevier
Publication Date
Volume
59
Issue
6
Identifiers
DOI: 10.1016/j.sysconle.2010.03.007
Keywords
  • Behavioural Systems Theory
  • Quadratic Differential Forms
  • Lossless Electrical Networks
  • Lossless Positive Real Transfer Functions
  • Linear Lossless Systems
  • Oscillatory Behaviours

Abstract

Abstract In this paper, motivated by the phenomenon of the interconnection of lossless electrical networks, a class of behaviours known as J -lossless behaviours is introduced, where J is a symmetric two-variable polynomial matrix. It is shown that for certain values of J , interconnection of J -lossless behaviours leads to an oscillatory behaviour. Physically this translates to the fact that interconnection of two multi-port lossless electrical networks results in an autonomous lossless electrical network. Finally, the problem of decomposition of an oscillatory behaviour with a given characteristic polynomial as an interconnection of two single-input–single-output behaviours, such that one has a lossless positive real transfer function and the other has a lossless negative real transfer function is also considered. This problem can be viewed as an inverse problem to the one of interconnection of J -lossless behaviours.

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