Nonsmooth dynamics analysis of a switching controlled system

The switching control strategy needs to design the switching-surface and the control signal. In this paper, the control effect and the control process are studied for different control strategy based on dynamics method. For autonomous van der pol system, the orbit can be suppressed to an equilibrium when the switching-surface is chose to include equilibrium; otherwise the orbit only can be controlled to a sliding limit cycle of small amplitude. Crossing-sliding bifurcation and switching-sliding bifurcation is common route from crossing orbit to full-sliding orbit, and grazing-sliding bifurcation is common route from crossing orbit to equilibrium. The control strategy is robust to the disturbance of parameter and control signal once the steady full-sliding orbit is achieved.