H∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach

Emilia Fridman; Yury Orlov

doi:10.1109/CDC.2008.4738827

H_∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach

Emilia Fridman^*, Yury Orlov

^*Corresponding author for this work

School of Electrical Engineering

Centro de Investigacion Cientifica y de Educacion Superior de Ensenada

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

2 Scopus citations

Abstract

Exponential stability analysis and L₂-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for an uncertain heat conduction equation and for an uncertain wave equation. These conditions are then utilized to synthesize H_∞ static output-feedback boundary controllers of the systems in question.

Original language	English
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	853-858
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4738827
State	Published - 2008
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: 9 Dec 2008 → 11 Dec 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	9/12/08 → 11/12/08

Keywords

Distributed parameter systems
LMI
Lyapunov functional
Stability

Access to Document

10.1109/CDC.2008.4738827

Cite this

Fridman, E., & Orlov, Y. (2008). H_∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 853-858). Article 4738827 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4738827

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abstract = "Exponential stability analysis and L2-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for an uncertain heat conduction equation and for an uncertain wave equation. These conditions are then utilized to synthesize H∞ static output-feedback boundary controllers of the systems in question.",

keywords = "Distributed parameter systems, LMI, Lyapunov functional, Stability",

author = "Emilia Fridman and Yury Orlov",

year = "2008",

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Fridman, E & Orlov, Y 2008, H_∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4738827, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 853-858, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 9/12/08. https://doi.org/10.1109/CDC.2008.4738827

H_∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach. / Fridman, Emilia; Orlov, Yury.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 853-858 4738827 (Proceedings of the IEEE Conference on Decision and Control).

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

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N2 - Exponential stability analysis and L2-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for an uncertain heat conduction equation and for an uncertain wave equation. These conditions are then utilized to synthesize H∞ static output-feedback boundary controllers of the systems in question.

AB - Exponential stability analysis and L2-gain analysis are developed for uncertain distributed parameter systems. Scalar heat processes and distributed mechanical oscillators, governed by semilinear partial differential equations of parabolic and, respectively, hyperbolic types, are chosen for treatment. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for an uncertain heat conduction equation and for an uncertain wave equation. These conditions are then utilized to synthesize H∞ static output-feedback boundary controllers of the systems in question.

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Fridman E, Orlov Y. H_∞ boundary control of semilinear heat processes and distributed mechanical oscillators: An LMI approach. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc. 2008. p. 853-858. 4738827. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2008.4738827