Every storage function is a state function

H.L. Trentelman, J.C. Willems

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It is shown that for linear dynamical systems with quadratic supply rates, a storage function can always be written as a quadratic function of the state of an associated linear dynamical system. This dynamical system is obtained by combining the dynamics of the original system with the dynamics of the supply rate. (C) 1997 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)249-259
Number of pages11
JournalSystems & Control Letters
Issue number5
Publication statusPublished - 19-Dec-1997


  • dissipative dynamical systems
  • state
  • storage function
  • quadratic differential forms
  • two-variable polynomial matrices

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