Feedback linearization: Difference between revisions

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Lie derivative: the d in the derivate shoud always be \mathrm{d} not \operatorname{d} to prevent the spacing
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where <math>x \in \mathbb{R}^n</math> is the state vector, <math>u \in \mathbb{R}^p</math> is the vector of inputs, and <math>y \in \mathbb{R}^m</math> is the vector of outputs. The goal is to develop a control input
:<math>u = a(x) + b(x)v\,</math>
that renders a linear input&ndash;output map between the new input <math>vu</math> and the output. An outer-loop control strategy for the resulting linear control system can then be applied.