Passive linear continuous-time systems: Characterization through structure

Izchak Lewkowicz

doi:10.1016/j.sysconle.2020.104816

Passive linear continuous-time systems: Characterization through structure

Izchak Lewkowicz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the discrete-time case, the corresponding structure is of a maximal matrix-convex set, closed under multiplication among its elements.

Original language	English
Article number	104816
Journal	Systems and Control Letters
Volume	147
DOIs	https://doi.org/10.1016/j.sysconle.2020.104816
State	Published - 1 Jan 2021

Keywords

Electrical circuits
K–Y–P Lemma
Matrix-convex sets
Passive linear systems
Positive real rational functions
State-space realization

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/j.sysconle.2020.104816

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title = "Passive linear continuous-time systems: Characterization through structure",

abstract = "We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the discrete-time case, the corresponding structure is of a maximal matrix-convex set, closed under multiplication among its elements.",

keywords = "Electrical circuits, K{\textendash}Y{\textendash}P Lemma, Matrix-convex sets, Passive linear systems, Positive real rational functions, State-space realization",

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N2 - We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the discrete-time case, the corresponding structure is of a maximal matrix-convex set, closed under multiplication among its elements.

AB - We here show that the family of finite-dimensional, continuous-time, passive, linear, time-invariant systems can be characterized through the structure of maximal matrix-convex cones, closed under inversion. Moreover, this observation unifies three setups: (i) differential inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the discrete-time case, the corresponding structure is of a maximal matrix-convex set, closed under multiplication among its elements.

KW - Electrical circuits

KW - K–Y–P Lemma

KW - Matrix-convex sets

KW - Passive linear systems

KW - Positive real rational functions

KW - State-space realization

UR - https://www.scopus.com/pages/publications/85096843239

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DO - 10.1016/j.sysconle.2020.104816

M3 - Article

AN - SCOPUS:85096843239

SN - 0167-6911

VL - 147

JO - Systems and Control Letters

JF - Systems and Control Letters

M1 - 104816

ER -

Passive linear continuous-time systems: Characterization through structure

Abstract

Keywords

ASJC Scopus subject areas

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