Feedback linearization: Difference between revisions

Revision as of 14:35, 18 July 2014

Revision as of 13:41, 17 November 2014

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=== Relative degree ===

In our feedback linearized system made up of a state vector of the output <math>y</math> and its first <math>(n-1)</math> derivatives, we must understand how the input <math>u</math> enters the system. To do this, we introduce the notion of [[relative degree]]. Our system given by (1) and (2) is said to have relative degree <math>r \in \mathbb{W}</math> at a point <math>x_0</math> if,

:<math>L_{g}L_{f}^{k}h(x) = 0 \qquad \forall x</math> in a [[neighbourhood (mathematics)|neighbourhood]] of <math>x_0</math> and all <math>k \leq r-2</math>