On output tracking for nonlinear systems with singular points

In this paper we design a continuous control law that achieves approximate output tracking of a large class of reference signals for nonlinear systems containing singular points in their state trajectory. Our approach is based on exact and approximate input-output linearization techniques and uses a switching control law which is smooth and guarantees all the states remain bounded. An example is provided to illustrate how these results can be used to globally track a reference signal with approximate tracking through singular points.