Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs

Yusuke Matsuda; Yoshio Ebihara; Tomomichi Hagiwara

doi:10.1109/CDC.2009.5399826

Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs

Yusuke Matsuda, Yoshio Ebihara, Tomomichi Hagiwara

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

1 Citation (Scopus)

Abstract

This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

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	2174-2179
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399826
Publication status	Published - 2009
Externally published	Yes
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

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

Other

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

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5399826

Cite this

Matsuda, Y., Ebihara, Y., & Hagiwara, T. (2009). Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 2174-2179). Article 5399826 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399826

Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. / Matsuda, Yusuke; Ebihara, Yoshio; Hagiwara, Tomomichi.
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. 2174-2179 5399826 (Proceedings of the IEEE Conference on Decision and Control).

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

Matsuda, Y, Ebihara, Y & Hagiwara, T 2009, Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399826, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2174-2179, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5399826

Matsuda Y, Ebihara Y, Hagiwara T. Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. 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. 2174-2179. 5399826. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399826

Matsuda, Yusuke ; Ebihara, Yoshio ; Hagiwara, Tomomichi. / Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. 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. 2174-2179 (Proceedings of the IEEE Conference on Decision and Control).

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abstract = "This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.",

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N2 - This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

AB - This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

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Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs

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