Lyapunov Theory: Find Unique Equil Pt.

  • #1
ceomtcl
14
0
Lyapunov Theory: Please Help!

Homework Statement


If the origin x=0 is globally asymptotically stable equilibrium point of the system then it must be the _________ equilibrium point of the system.


Homework Equations



None

The Attempt at a Solution



This is an objective/one word answer.
 
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  • #2


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!
 
  • #3


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?
 
  • #4


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?
 
  • #5


sounds right to me! :smile:
 
  • #6


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

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