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Robustness analysis and synthesis for nonlinear uncertain systems

Lu, Wei-Min and Doyle, John C. (1997) Robustness analysis and synthesis for nonlinear uncertain systems. IEEE Transactions on Automatic Control, 42 (12). pp. 1654-1662. ISSN 0018-9286. https://resolver.caltech.edu/CaltechAUTHORS:20190318-151348243

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Abstract

A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of nonlinear systems subject to L_2-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem. As in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the solvability of robustness synthesis problems are represented in terms of NLMIs as well. With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favourable.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/9.650015DOIArticle
ORCID:
AuthorORCID
Doyle, John C.0000-0002-1828-2486
Additional Information:© 1997 IEEE. Manuscript received February 24, 1995; revised March 18, 1997. Recommended by Associate Editor, M. A. Dahleh. This work was supported in part by AFOSR. The authors would like to thank Y. Huang for her help with the implementation of the finite difference algorithm in Example V.2.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Subject Keywords:Computational nonlinear control, nonlinear control systems, nonlinear matrix inequality (NLMI), robust control, robust performance, state space
Issue or Number:12
Record Number:CaltechAUTHORS:20190318-151348243
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190318-151348243
Official Citation:Wei-Min Lu and J. C. Doyle, "Robustness analysis and synthesis for nonlinear uncertain systems," in IEEE Transactions on Automatic Control, vol. 42, no. 12, pp. 1654-1662, Dec. 1997. doi: 10.1109/9.650015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93943
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Mar 2019 22:49
Last Modified:03 Oct 2019 20:59

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