Storage functions for dissipative linear systems are quadratic state functions

HL Trentelman; JC Willems

Storage functions for dissipative linear systems are quadratic state functions

HL Trentelman^*, JC Willems

^*Corresponding author for this work

Faculty of Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

5 Citations (Scopus)

Abstract

This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.

Original language	English
Title of host publication	PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5
Place of Publication	NEW YORK
Publisher	IEEE (The Institute of Electrical and Electronics Engineers)
Pages	42-47
Number of pages	6
ISBN (Print)	0-7803-4187-2
Publication status	Published - 1997
Event	36th IEEE Conference on Decision and Control - , Canada Duration: 10-Dec-1997 → 12-Dec-1997

Publication series

Name	IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS
Publisher	IEEE
ISSN (Print)	0191-2216

Other

Other	36th IEEE Conference on Decision and Control
Country/Territory	Canada
Period	10/12/1997 → 12/12/1997

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@inproceedings{ef7c3d93951c463995eaf8f10f8b599b,

title = "Storage functions for dissipative linear systems are quadratic state functions",

abstract = "This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.",

author = "HL Trentelman and JC Willems",

year = "1997",

language = "English",

isbn = "0-7803-4187-2",

series = "IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS",

publisher = "IEEE (The Institute of Electrical and Electronics Engineers)",

pages = "42--47",

booktitle = "PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5",

note = "36th IEEE Conference on Decision and Control ; Conference date: 10-12-1997 Through 12-12-1997",

}

Trentelman, HL & Willems, JC 1997, Storage functions for dissipative linear systems are quadratic state functions. in PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5. IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS, IEEE (The Institute of Electrical and Electronics Engineers), NEW YORK, pp. 42-47, 36th IEEE Conference on Decision and Control, Canada, 10/12/1997.

Storage functions for dissipative linear systems are quadratic state functions. / Trentelman, HL; Willems, JC.
PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5. NEW YORK: IEEE (The Institute of Electrical and Electronics Engineers), 1997. p. 42-47 (IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Storage functions for dissipative linear systems are quadratic state functions

AU - Trentelman, HL

AU - Willems, JC

PY - 1997

Y1 - 1997

N2 - This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.

AB - This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage function. The supply rate is the rate at which energy flows into the system, a storage function is a function that measures the amount of enery that is stored inside the system. In this paper, we will argue that for linear dynamical systems with quadratic supply rates, any storage function can be represented as a quadratic function of any state variable of a linear dynamical system whose dynamics is obtained by combining the dynamics of the original system, and the dynamics of the supply rate.

M3 - Conference contribution

SN - 0-7803-4187-2

T3 - IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS

SP - 42

EP - 47

BT - PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5

PB - IEEE (The Institute of Electrical and Electronics Engineers)

CY - NEW YORK

T2 - 36th IEEE Conference on Decision and Control

Y2 - 10 December 1997 through 12 December 1997

ER -

Storage functions for dissipative linear systems are quadratic state functions

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