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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 127185, 6 pages
Research Article

Viability Discrimination of a Class of Control Systems on a Nonsmooth Region

1School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 27 July 2013; Revised 16 December 2013; Accepted 18 December 2013; Published 12 January 2014

Academic Editor: Zhigang Jiang

Copyright © 2014 Na Zhao 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.


The viability problem is an important field of study in control theory; the corresponding research has profound significance in both theory and practice. In this paper, we consider the viability for both an affine nonlinear hybrid system and a hybrid differential inclusion on a region with subdifferentiable boundary. Based on the nonsmooth analysis theory, we obtain a method to verify the viability condition at a point, when the boundary function of the region is subdifferentiable and its subdifferential is convex hull of many finite points.