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A State-Space Approach to Robustness Analysis and Synthesis for Nonlinear Uncertain Systems

Lu, Wei-Min and Doyle, John C. (1994) A State-Space Approach to Robustness Analysis and Synthesis for Nonlinear Uncertain Systems. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1994.010

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Abstract

A state-space characterization of stability and performance robustness analysis and synthesis with some computationally attractive properties for nonlinear uncertain systems is proposed. The robust stability and robust performances for a class of nonlinear systems subject to bounded structured uncertainties are characterized in terms of various types of nonlinear matrix inequalities (NLMIs), which are natural generalizations of the linear matrix inequalities (LMIs) that appear in linear robustness analysis. As in the linear case, scalings or multipliers are used to find storage functions that give sufficient conditions for robust performances; these are also necessary under certain assumptions about smoothness of the storage functions and structure of the uncertainty. The resulting NLMIs yield convex optimization problems. Unlike the linear case, these convex problems are not finite dimensional, so their computational benefits are far less immediate. Sufficient conditions for the solvability of robust synthesis problems are developed in terms of NLMIs as well. Some aspects of the computational issues are also discussed.


Item Type:Report or Paper (Technical Report)
Additional Information:The authors would like to thank J.W. Helton and J.S. Shamma for fruitful and extensive discussions. They also gratefully acknowledge helpful comments about the original version of this paper from Y.Huang, J.Morris, and K.Zhou. Support for this work was provided by NSF, AFOSR, and ONR.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1994.010
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1994.010
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28076
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:12 Sep 2006
Last Modified:26 Dec 2012 14:30

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