This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: u ( t ) = sgn( x 1 ( t ) + . 5 x 2 ( t ) 2 sgn( x 2 ( t ))) . (Do you know why ?) (a) Find a Lyapunov function V : R 2 R 2 for the closed loop system, such that V ( x ( t )) is strictly decreasing along all solutions of system equations except the equilibrium solution x ( t ) 0. (b) Find out whether the equilibrium remains asymptotically stable when the same controller is used for the perturbed system x 1 ( t ) = x 2 ( t ) ,  u ( t )  1 , x 2 ( t ) = x 1 ( t ) + u ( t ) , where &gt; is small....
View
Full
Document
This note was uploaded on 11/07/2011 for the course AERO 16.36 taught by Professor Alexandremegretski during the Spring '09 term at MIT.
 Spring '09
 AlexandreMegretski
 Dynamics

Click to edit the document details