Passive linear discrete-time systems: Characterization through structure

Izchak Lewkowicz

doi:10.1016/j.laa.2021.02.006

Passive linear discrete-time systems: Characterization through structure

Izchak Lewkowicz

Department of Electrical & Computer Engineering

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

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	299-315
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	623
DOIs	https://doi.org/10.1016/j.laa.2021.02.006
State	Published - 15 Aug 2021

Keywords

Discrete-time bounded real rational functions
Kalman-Yakubovich-Popov lemma
Matrix-convex sets
Passive linear systems
State-space realization

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2021.02.006

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

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

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

KW - Discrete-time bounded real rational functions

KW - Kalman-Yakubovich-Popov lemma

KW - Matrix-convex sets

KW - Passive linear systems

KW - State-space realization

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SP - 299

EP - 315

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Passive linear discrete-time systems: Characterization through structure

Abstract

Keywords

ASJC Scopus subject areas

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