AN ALGEBRAIC APPROACH TO THE REALIZATION OF LOSSLESS NEGATIVE IMAGINARY BEHAVIORS

Shodhan Rao*, Paolo Rapisarda

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

We consider a behavior with an equal number of inputs and outputs for which there exists a quadratic differential form which is positive for nonzero trajectories of the behavior and whose derivative is equal to the scalar product of the input vector and the derivative of the output vector. Such systems occur, for example, when considering conservative mechanical systems. We give a method of computation of a state space realization from an observable image representation of such a behavior. We apply the insights derived from this realization procedure to the synthesis of lossless mechanical systems.

Original languageEnglish
Pages (from-to)1700-1720
Number of pages21
JournalSIAM Journal on Control and Optimization
Volume50
Issue number3
DOIs
Publication statusPublished - 2012

Keywords

  • behavioral systems theory
  • quadratic differential forms
  • conservative mechanical systems
  • lossless positive real transfer functions
  • lossless mechanical network synthesis
  • time-reversible Hamiltonian systems
  • SYSTEMS

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