### 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.

Original language | Undefined |
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Pages (from-to) | 323-332 |

Number of pages | 10 |

Journal | Systems and control letters |

Volume | 59 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2010 |

### Keywords

- Oscillatory behaviours
- EWI-18114
- Behavioural systems theory
- Linear lossless systems
- IR-72318
- Lossless positive real transfer functions
- Quadratic differential forms
- METIS-270901
- Lossless electrical networks

## Cite this

Rao, S. (2010). Interconnection of J-lossless behaviours.

*Systems and control letters*,*59*(6), 323-332. https://doi.org/10.1016/j.sysconle.2010.03.007