Quantitatively hyper-positive real functions

Daniel Alpay; Izchak Lewkowicz

doi:10.1016/j.laa.2020.11.014

Quantitatively hyper-positive real functions

Daniel Alpay, Izchak Lewkowicz

Department of Electrical & Computer Engineering

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

2 Scopus citations

Abstract

Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

Original language	English
Pages (from-to)	316-334
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	623
DOIs	https://doi.org/10.1016/j.laa.2020.11.014
State	Published - 15 Aug 2021

Keywords

Absolute stability
Convex invertible cones
Electrical circuits
Feedback loops
Hyper-positive real functions
K-Y-P lemma
Matrix-convex set
Positive real functions
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.2020.11.014

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title = "Quantitatively hyper-positive real functions",

abstract = "Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.",

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author = "Daniel Alpay and Izchak Lewkowicz",

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year = "2021",

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doi = "10.1016/j.laa.2020.11.014",

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T1 - Quantitatively hyper-positive real functions

AU - Alpay, Daniel

AU - Lewkowicz, Izchak

PY - 2021/8/15

Y1 - 2021/8/15

N2 - Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

AB - Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

KW - Absolute stability

KW - Convex invertible cones

KW - Electrical circuits

KW - Feedback loops

KW - Hyper-positive real functions

KW - K-Y-P lemma

KW - Matrix-convex set

KW - Positive real functions

KW - State-space realization

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U2 - 10.1016/j.laa.2020.11.014

DO - 10.1016/j.laa.2020.11.014

M3 - Article

AN - SCOPUS:85097664337

SN - 0024-3795

VL - 623

SP - 316

EP - 334

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Quantitatively hyper-positive real functions

Abstract

Keywords

ASJC Scopus subject areas

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