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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....
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 Spring '09
 AlexandreMegretski
 Dynamics, Massachusetts Institute of Technology, Stability theory, Department of Electrical Engineering and Computer Science, DYNAMICS OF NONLINEAR SYSTEMS, 6.243j

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