Feedback linearization is a common approach used in controlling nonlinear systems. The approach involves coming up with a transformation of the nonlinear system into an equivalent linear system through a change of variables and a suitable control input. Feedback linearization may be applied to nonlinear systems of the form
where is the state vector, is the vector of inputs, and is the vector of outputs. The goal is to develop a control input
that renders a linear input–output map between the new input and the output. An outer-loop control strategy for the resulting linear control system can then be applied.