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Mathematical Problems in Engineering
Volume 2013, Article ID 523527, 9 pages
Research Article

Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input

Instituto Tecnológico de Chihuahua, Avenida Tecnológico 2909, 31310 Chihuahua, CHIH, Mexico

Received 27 July 2013; Revised 4 October 2013; Accepted 6 October 2013

Academic Editor: Xudong Zhao

Copyright © 2013 Pedro R. Acosta. 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 deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.