# Lect_28 - Nonlinear Systems and Control Lecture # 28...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 28 Stabilization Backstepping p. 1/ ? ? = f ( ) + g ( ) = u, R n , , u R Stabilize the origin using state feedback View as virtual control input to = f ( ) + g ( ) Suppose there is = ( ) that stabilizes the origin of = f ( ) + g ( ) ( ) V [ f ( ) + g ( ) ( )] W ( ) , D p. 2/ ? ? z = ( ) = [ f ( ) + g ( ) ( )] + g ( ) z z = u [ f ( ) + g ( ) ] u = [ f ( ) + g ( ) ] + v = [ f ( ) + g ( ) ( )] + g ( ) z z = v p. 3/ ? ? V c ( , ) = V ( ) + 1 2 z 2 V c = V [ f ( ) + g ( ) ( )] + V g ( ) z + zv W ( ) + V g ( ) z + zv v = V g ( ) kz, k > V c W ( ) kz 2 p. 4/ ? ? Example x 1 = x 2 1 x 3 1 + x 2 ,...
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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_28 - Nonlinear Systems and Control Lecture # 28...

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