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Mathematical Problems in Engineering
Volume 2015, Article ID 319495, 7 pages
Research Article

Adaptive Second-Order Sliding Mode Control Design for a Class of Nonlinear Systems with Unknown Input

1Ningbo University of Technology, Ningbo 315000, China
2School of Astronautics, Harbin Institute of Technology, Harbin 150000, China
3Laboratoire OPERA, Universite de Technologie de Belfort-Montbeliard, 90010 Belfort, France
4Ningbo Academy of Smart City Development, Ningbo 315000, China

Received 7 March 2015; Accepted 20 April 2015

Academic Editor: Xinggang Yan

Copyright © 2015 You Zheng et al. 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.


An adaptive second-order sliding mode controller is proposed for a class of nonlinear systems with unknown input. The proposed controller continuously drives the sliding variable and its time derivative to zero in the presence of disturbances with unknown boundaries. A Lyapunov approach is used to show finite time stability for the system in the presence of a class of uncertainty. An illustrative simulation example is presented to demonstrate the performance and robustness of the proposed controller.