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Published December 1997 | Published
Journal Article Open

Robustness analysis and synthesis for nonlinear uncertain systems

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.

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.

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