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m →Relative degree: Wikified poles and zeros. Changed < r-1 too leq r-2. Made it clear that r is a whole number. |
m Use align for system. |
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''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 following form:
:<math>\begin{align}\dot{x} &= f(x) + g(x)u \qquad &(1)\
▲:<math>y = h(x) \qquad \qquad \qquad (2)</math>
Where <math>x \in R^n</math> is the state vector, <math>u \in R^p</math> is the vector of inputs, and <math>y \in R^m</math> is the vector of outputs. The goal, then, is to develop a control input <math>u</math> that renders either the input-output map linear, or results in a linearization of the full state of the system.
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