
This paper presents a design method for controlling multiple sliding surfaces of nonlinear systems with matched uncertainty using a single actuator. Sliding mode control, in general, requires one actuator for every control objective. Compared to the vast literature on sliding mode control, there has been little work on general theories that can be applied to underactuated nonlinear control. A sufficient condition to guarantee simultaneous robust stabilization of multiple surfaces is derived. A corollary is presented for the case when the sliding surfaces are affine in the control. An example of an overhead crane is presented to validate the design method.
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