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Unformatted text preview: Nonlinear Systems and Control Lecture # 24 Observer, Output Feedback & Strict Feedback Forms – p. 1/1 2 Definition: A nonlinear system is in the observer form if ˙ x = Ax + γ ( y,u ) , y = Cx where ( A,C ) is observable Observer: ˙ ˆ x = A ˆ x + γ ( y,u ) + H ( y − C ˆ x ) ˜ x = x − ˆ x ˙ ˜ x = ( A − HC )˜ x Design H such that ( A − HC ) is Hurwitz – p. 2/1 2 Theorem: An ndimensional singleoutput (SO) system ˙ x = f ( x ) + g ( x ) u, y = h ( x ) is transformable into the observer form if and only if there is a domain D such that rank bracketleftbigg ∂φ ∂x ( x ) bracketrightbigg = n, ∀ x ∈ D where φ = bracketleftBig h, L f h, ··· L n − 1 f h bracketrightBig T and the unique vector field solution τ of ∂φ ∂x τ = b, where b = bracketleftBig , ··· , 1 bracketrightBig T – p. 3/1 2 satisfies [ ad i f τ,ad j f τ ] = 0 , ≤ i,j ≤ n − 1 and [ g,ad j f τ ] = 0 , ≤ j ≤ n − 2 The change of variables z = T ( x ) is given by ∂T ∂x...
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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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