Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems

Yoshio Ebihara, Yusuke Matsuda, Tomomichi Hagiwara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the preceding studies we proposed a dual LMI approach for robust performance analysis problems of LTI systems that are affected by parametric uncertainties. By starting from a dual LMI that characterizes a dissipation performance of uncertainty-free LTI systems, we showed that the robust dissipation performance analysis problem can be reduced into a feasibility problem of a polynomial matrix inequality (PMI). Moreover, by applying a linearization to the PMI, we derived an infinite sequence of LMI relaxation problems that allows us to reduce the relaxation gap gradually. Nevertheless, the asymptotic behaviour of this infinite sequence has been open, and this motivates us to study mutual relationship among the dual LMI approach and existing approaches. As the main result of this paper, we prove that our dual LMI approach corresponds to the dual of the polynomial parameter-dependent Lyapunov function approach with matrix sum-of-squares (SOS) relaxations, which is known to be asymptotically exact. Thus we clarify a close relationship between these two approaches that are seemingly very different. This relationship readily leads us to the desired conclusion that the proposed dual LMI approach is asymptotically exact as well.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages1472-1477
Number of pages6
DOIs
Publication statusPublished - Dec 1 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

LMI Approach
Robust Performance
Uncertain systems
Exactness
Uncertain Systems
Performance Analysis
Polynomials
Polynomial Matrices
Lyapunov functions
Linearization
Matrix Inequality
Dissipation
Parameter-dependent Lyapunov Function
Parametric Uncertainty
Sum of squares
Asymptotic Behavior
Uncertainty
Polynomial
Relationships

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Ebihara, Y., Matsuda, Y., & Hagiwara, T. (2010). Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 1472-1477). [5717776] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717776

Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems. / Ebihara, Yoshio; Matsuda, Yusuke; Hagiwara, Tomomichi.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1472-1477 5717776 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ebihara, Y, Matsuda, Y & Hagiwara, T 2010, Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717776, Proceedings of the IEEE Conference on Decision and Control, pp. 1472-1477, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717776
Ebihara Y, Matsuda Y, Hagiwara T. Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1472-1477. 5717776. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717776
Ebihara, Yoshio ; Matsuda, Yusuke ; Hagiwara, Tomomichi. / Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 1472-1477 (Proceedings of the IEEE Conference on Decision and Control).
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