Switching Dynamics of a Periodically Forced Discontinuous System with an Inclined Boundary

Albert C. J. Luo, and Brandon M. Rapp
Department of Mechanical and Industrial Engineering
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1805, USA
aluo@siue.edu and brapp4@gmail.com

This paper presented the switching dynamics of flow from one domain into another one in discontinuous dynamical system with an inclined line boundary governed by a control law. The normal vector field product for flow switching are introduced, and the corresponding conditions for switability, sliding and grazing will be developed. In addition, periodic motions for such a system is predicted, and the stability and bifurcation analysis will be carried out. Numerical illustrations of periodic motions and chaos are presented. This investigation will provide a different way to look into sliding mode control.