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Lyapunov Theory: Please Help

  1. Nov 1, 2008 #1
    Lyapunov Theory: Please Help!!!

    1. The problem statement, all variables and given/known data
    If the origin x=0 is globally asymptotically stable equilibrium point of the system then it must be the _________ equilibrium point of the system.


    2. Relevant equations

    None

    3. The attempt at a solution

    This is an objective/one word answer.
     
  2. jcsd
  3. Nov 1, 2008 #2
    Re: Lyapunov Theory

    I have around 50 such objective questions for the assignments. I am done with 40 plus, but a few of these are haunting ms and i am not sure about them! Any help is highly appreciated!
     
  4. Nov 1, 2008 #3

    gabbagabbahey

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    Re: Lyapunov Theory: Please Help!!!

    Hint: If the point x=0 is a "globally asymptotically stable equilibrium point", what happens as you approach x=0 from any direction, from any starting point? Can there be any other equilibrium points?
     
  5. Nov 2, 2008 #4
    Re: Lyapunov Theory: Please Help!!!

    1. I believe that if the point x=0 is a "globally asymptotically stable equilibrium point" then if we approach x=0 from any direction then it will converge to equilibrium point. Am I right?

    2. According to me, there is no other equilibrium point.

    Please let me know if i am right?
     
  6. Nov 2, 2008 #5

    gabbagabbahey

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    Re: Lyapunov Theory: Please Help!!!

    sounds right to me! :smile:
     
  7. Nov 2, 2008 #6
    Re: Lyapunov Theory: Please Help!!!

    So, the blank should be "only". Just wanted to confirm if it is what you want to say.
     
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