Lect_27 - Nonlinear Systems and Control Lecture # 27...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 27 Stabilization Partial Feedback Linearization p. 1/1 1 Consider the nonlinear system x = f ( x ) + G ( x ) u [ f (0) = 0] Suppose there is a change of variables z = bracketleftBigg bracketrightBigg = T ( x ) = bracketleftBigg T 1 ( x ) T 2 ( x ) bracketrightBigg defined for all x D R n , that transforms the system into = f ( , ) = A + B ( x )[ u ( x )] ( A,B ) is controllable and ( x ) is nonsingular for all x D p. 2/1 1 u = ( x ) + 1 ( x ) v = f ( , ) , = A + Bv Suppose the origin of = f ( , 0) is asymptotically stable v = K, where ( A BK ) is Hurwitz Lemma 13.1: The origin of = f ( , ) , = ( A BK ) is asymptotically stable if the origin of = f ( , 0) is asymptotically stable Proof: V ( , ) = V 1 ( )+ k radicalbig T P p. 3/1 1 If the origin of = f ( , 0) is globally asymptotically stable, will the origin of...
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This note was uploaded on 07/25/2008 for the course ME 859 taught by Professor Choi during the Spring '08 term at Michigan State University.

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Lect_27 - Nonlinear Systems and Control Lecture # 27...

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