Lyapunov Theory: Find Unique Equil Pt.

[ceomtcl]

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.

 

[ceomtcl]

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!

 

[gabbagabbahey]

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?

 

[ceomtcl]

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?

 

[gabbagabbahey]

sounds right to me!

 

[ceomtcl]

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