Abstract
In this chapter, the sliding and transversality of a flow at a boundary from one domain into another in discontinuous dynamical systems will be presented through a periodically forced, discontinuous dynamical system. The inclined line boundary in phase space will be considered for the dynamical system to switch. The normal vector-field for flow switching on the separation boundary will be introduced. The transversality condition of a flow to the separation boundary will be achieved through such normal vector fields, and the sliding and grazing conditions to the separation boundary will be presented as well. Using mapping structures, the periodic motions in such a discontinuous system will be predicted analytically. With the analytical conditions of grazing and sliding motions, the parameter maps of specific motions will be developed. Illustrations of periodic and chaotic motions are given, and the normal vector fields will be presented to show the analytical conditions. The results presented in this chapter may help one better understand the sliding mode control.
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© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
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(2009). Transversality and Sliding Phenomena. In: Discontinuous Dynamical Systems on Time-varying Domains. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00253-3_3
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DOI: https://doi.org/10.1007/978-3-642-00253-3_3
Publisher Name: Springer, Berlin, Heidelberg
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