{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lect_26 - Nonlinear Systems and Control Lecture 26...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 + Bγ ( x )[ u − α ( x )] where ( A,B ) is controllable and γ ( x ) is nonsingular for all x ∈ D u = α ( x ) + γ − 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 closed-loop system ˙ z = ( A − BK ) z is globally exponentially stable u = α ( x ) − γ − 1 ( x ) KT ( x ) Closed-loop system in the x-coordinates: ˙ x = f ( x ) + G ( x ) bracketleftbig α ( x ) − γ − 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 α ( x ) − γ − 1 ( x ) KT ( x ) bracketrightbig x = 0 is asymptotically stable because...
View Full Document

{[ snackBarMessage ]}