When is an Equilibrium Point Isolated in a Simple Linear Time Invariant System?

[ceomtcl]

Homework Statement

Given a simplest linear time invariant system (x dot = Ax), with an Equilibrium Point at the origin; when is the Equilibrium Point isolated?

Homework Equations

None

The Attempt at a Solution

Conceptual Question

 

[gabbagabbahey]

Start with the definition of an isolated equilibrium point...

 

[ceomtcl]

Can you please redefine it for me? may be i am missing something important?

 

[gabbagabbahey]

How about you start by posting whichever definition you have in your text/notes (word for word if possible)

 

[ceomtcl]

I know that the linear system can have only one isolated equilibrium point, thus it can have only one steady state operating point that attracts the state of the system irrespective of the initial state. However a non linear system can have more than one isolated equilibrium point.

 

[ceomtcl]

Does it mean that the Equilibrium point is isolated when it is stable?

 

[gabbagabbahey]

It means that if there is an equilibrium point of this linear system, it is an isolated point...so is there an equilibrium point for this system?...Under what circumstances?

 

[ceomtcl]

ok, i think i understood it, Thanks a lot for the help!