LMI relaxations for non-quadratic discrete stabilization via pólya theorem

Ji Chang Lo; Chin Fu Tsai

doi:10.1109/CDC.2009.5399994

LMI relaxations for non-quadratic discrete stabilization via pólya theorem

Ji Chang Lo, Chin Fu Tsai

Department of Mechanical Engineering

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

3 Scopus citations

Abstract

In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Pólya's Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7430-7435
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399994
State	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009

Publication series

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

Conference

Conference	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	15/12/09 → 18/12/09

Keywords

Homogeneous polynomials
Linear matrix inequality (LMI)
Parameter-dependent LMIs (PD-LMIs)
Relaxation

Access to Document

10.1109/CDC.2009.5399994

Cite this

Lo, J. C., & Tsai, C. F. (2009). LMI relaxations for non-quadratic discrete stabilization via pólya theorem. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 7430-7435). [5399994] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399994

Lo, Ji Chang ; Tsai, Chin Fu. / LMI relaxations for non-quadratic discrete stabilization via pólya theorem. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 7430-7435 (Proceedings of the IEEE Conference on Decision and Control).

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title = "LMI relaxations for non-quadratic discrete stabilization via p{\'o}lya theorem",

abstract = "In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of P{\'o}lya's Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.",

keywords = "Homogeneous polynomials, Linear matrix inequality (LMI), Parameter-dependent LMIs (PD-LMIs), Relaxation",

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Lo, JC & Tsai, CF 2009, LMI relaxations for non-quadratic discrete stabilization via pólya theorem. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399994, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 7430-7435, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 15/12/09. https://doi.org/10.1109/CDC.2009.5399994

LMI relaxations for non-quadratic discrete stabilization via pólya theorem. / Lo, Ji Chang; Tsai, Chin Fu.

Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 7430-7435 5399994 (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 - In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Pólya's Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.

AB - In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Pólya's Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.

KW - Homogeneous polynomials

KW - Linear matrix inequality (LMI)

KW - Parameter-dependent LMIs (PD-LMIs)

KW - Relaxation

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Lo JC, Tsai CF. LMI relaxations for non-quadratic discrete stabilization via pólya theorem. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 7430-7435. 5399994. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399994

LMI relaxations for non-quadratic discrete stabilization via pólya theorem

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