A polynomial approach to the realization of J-lossless behaviours

S. Rao, Paolo Rapisarda, Lewis Moody

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    Abstract

    In this paper, a class of behaviours known as J-lossless behaviours is introduced, where J is a symmetric two-variable polynomial matrix. For a certain J, it is shown that the resulting set of J-lossless behaviours are SISO behaviours such that for each of such behaviours, there exists a quadratic differential form which is positive for nonzero trajectories of the behaviour and whose derivative is equal to the product of the input variable and the derivative of the output variable. Earlier, Van der Schaft and Oeloff had considered a specific form of realization for such behaviours that plays an important role in their model reduction procedure. In our paper, we give a method of computation of a state space realization from a transfer function of such a behaviour in the same form as considered by Van der Schaft and Oeloff, using polynomial algebraic methods. Apart from being useful in enlarging the scope of the model reduction procedure of Van der Schaft and Oeloff, we show that our method of realization also has application in the synthesis of lossless mechanical systems with given transfer functions using springs and masses.
    Original languageUndefined
    Title of host publication19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
    Place of PublicationBudapest, Hungary
    PublisherEötvös Loránd University (ELTE) and MTA SZTAKI (Computer and Automation Research Institute, Hungarian Academy of Sciences)
    Pages1911-1918
    Number of pages8
    ISBN (Print)978-963-311-370-7
    Publication statusPublished - Jul 2010
    Event19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010 - Budapest, Hungary
    Duration: 5 Jul 20109 Jul 2010
    Conference number: 19

    Publication series

    Name
    PublisherEötvös Loránd University (ELTE) and MTA SZTAKI (Computer and Automation Research Institute, Hungarian Academy of Sciences)

    Conference

    Conference19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
    Abbreviated titleMTNS
    CountryHungary
    CityBudapest
    Period5/07/109/07/10

    Keywords

    • METIS-271000
    • EWI-18339
    • Mechanical network synthesis
    • IR-73167

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