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Unformatted text preview: Nonlinear Systems and Control Lecture # 26 Stabilization Feedback Lineaization p.1/12 Consider the nonlinear system x = f ( x ) + G ( x ) u f (0) = 0 , x R n , u R m Suppose there is a change of variables z = T ( x ) , defined for all x D R n , that transforms the system into the controller form z = Az + B ( x )[ u ( x )] where ( A,B ) is controllable and ( x ) is nonsingular for all x D u = ( x ) + 1 ( x ) v z = Az + Bv p.2/12 v = Kz Design K such that ( A BK ) is Hurwitz The origin z = 0 of the closedloop system z = ( A BK ) z is globally exponentially stable u = ( x ) 1 ( x ) KT ( x ) Closedloop system in the xcoordinates: x = f ( x ) + G ( x ) bracketleftbig ( x ) 1 ( x ) KT ( x ) bracketrightbig p.3/12 What can we say about the stability of x = 0 as an equilibrium point of x = f ( x ) + G ( x ) bracketleftbig ( x ) 1 ( x ) KT ( x ) bracketrightbig x = 0 is asymptotically stable because...
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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.
 Spring '08
 CHOI

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