Stability and robust regulation of passive linear systems

Lassi Paunonen

doi:10.1137/17M1136407

Stability and robust regulation of passive linear systems

Lassi Paunonen^*

^*Corresponding author for this work

Computing Sciences

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

19 Citations (Scopus)

17 Downloads (Pure)

Abstract

We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and nonuniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for nonuniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.

Original language	English
Pages (from-to)	3827-3856
Number of pages	30
Journal	SIAM Journal on Control and Optimization
Volume	57
Issue number	6
DOIs	https://doi.org/10.1137/17M1136407
Publication status	Published - 2019
Publication type	A1 Journal article-refereed

Funding

∗Received by the editors June 27, 2017; accepted for publication (in revised form) September 17, 2019; published electronically November 26, 2019. https://doi.org/10.1137/17M1136407 Funding: This research was funded by the Academy of Finland grants 298182 and 310489. †Mathematics and Statistics, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101 Tampere, Finland ([email protected]). 1Here CΛ and CcΛ denote the Λ-extensions of C and Cc, respectively. See section 2 for details.

Keywords

Controller design
Coupled systems
Feedback
Impedance passive
Linear system
Polynomial stability
Robust output regulation
Strong stability
Strongly continuous semigroup

Publication forum classification

Publication forum level 2

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/17M1136407

Stability and robust regulation
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Cite this

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title = "Stability and robust regulation of passive linear systems",

abstract = "We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and nonuniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for nonuniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.",

keywords = "Controller design, Coupled systems, Feedback, Impedance passive, Linear system, Polynomial stability, Robust output regulation, Strong stability, Strongly continuous semigroup",

author = "Lassi Paunonen",

note = "Funding Information: ∗Received by the editors June 27, 2017; accepted for publication (in revised form) September 17, 2019; published electronically November 26, 2019. https://doi.org/10.1137/17M1136407 Funding: This research was funded by the Academy of Finland grants 298182 and 310489. †Mathematics and Statistics, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101 Tampere, Finland ([email protected]). 1Here CΛ and CcΛ denote the Λ-extensions of C and Cc, respectively. See section 2 for details. Publisher Copyright: {\textcopyright} 2019 Lassi Paunonen Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

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N1 - Funding Information: ∗Received by the editors June 27, 2017; accepted for publication (in revised form) September 17, 2019; published electronically November 26, 2019. https://doi.org/10.1137/17M1136407 Funding: This research was funded by the Academy of Finland grants 298182 and 310489. †Mathematics and Statistics, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101 Tampere, Finland ([email protected]). 1Here CΛ and CcΛ denote the Λ-extensions of C and Cc, respectively. See section 2 for details. Publisher Copyright: © 2019 Lassi Paunonen Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

N2 - We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and nonuniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for nonuniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.

AB - We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and nonuniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbance rejection for strongly stabilizable passive systems. In the case of nonsmooth reference and disturbance signals we present conditions for nonuniform rational and logarithmic rates of convergence of the output. The results are illustrated with examples on designing controllers for linear wave and heat equations, and on studying the stability of a system of coupled partial differential equations.

KW - Controller design

KW - Coupled systems

KW - Feedback

KW - Impedance passive

KW - Linear system

KW - Polynomial stability

KW - Robust output regulation

KW - Strong stability

KW - Strongly continuous semigroup

U2 - 10.1137/17M1136407

DO - 10.1137/17M1136407

M3 - Article

AN - SCOPUS:85062194568

SN - 0363-0129

VL - 57

SP - 3827

EP - 3856

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 6

ER -

Stability and robust regulation of passive linear systems

Abstract

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