Every storage function is a state function

H.L. Trentelman; J.C. Willems

Every storage function is a state function

H.L. Trentelman, J.C. Willems

Systems, Control and Applied Analysis

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Abstract

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 language	English
Pages (from-to)	249-259
Number of pages	11
Journal	Systems & Control Letters
Volume	32
Issue number	5
Publication status	Published - 19-Dec-1997

Keywords

dissipative dynamical systems
state
storage function
quadratic differential forms
two-variable polynomial matrices
LINEAR-SYSTEM
TIME-SERIES

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Cite this

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title = "Every storage function is a state function",

abstract = "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.",

keywords = "dissipative dynamical systems, state, storage function, quadratic differential forms, two-variable polynomial matrices, LINEAR-SYSTEM, TIME-SERIES",

author = "H.L. Trentelman and J.C. Willems",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",

year = "1997",

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journal = "Systems & Control Letters",

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T1 - Every storage function is a state function

AU - Trentelman, H.L.

AU - Willems, J.C.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1997/12/19

Y1 - 1997/12/19

N2 - 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.

AB - 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.

KW - dissipative dynamical systems

KW - state

KW - storage function

KW - quadratic differential forms

KW - two-variable polynomial matrices

KW - LINEAR-SYSTEM

KW - TIME-SERIES

M3 - Article

VL - 32

SP - 249

EP - 259

JO - Systems & Control Letters

JF - Systems & Control Letters

SN - 0167-6911

IS - 5

ER -