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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 736964, 9 pages
Research Article

Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities

School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 9 March 2013; Accepted 14 April 2013

Academic Editor: Zheng-Guang Wu

Copyright © 2013 Linna Zhou and Chunyu Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.