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# Nonlinear vs linear system

## Nonlinear vs linear system

(OP)
Hi all,

I have an "unstable nonlinear system" in my hand. I linearized it using two different operating points. The result is as follows:

The first linearized system is stable and the second is unstable.
Is that logical? Can a linear system be stable, although the nonlinear one is unstable?

eogut
Replies continue below

### RE: Nonlinear vs linear system

hi eogut
First of all, how did you decide that your nonlinear system is unstabel? did you simultate it and found that it is unstable?
Well, when you say that your nonlinear system is unstable, you are checking it at some initial point giving rise to unstability. That doesn't mean that it is  unstabel system. The system could have multiple solutions and could have different operatoing points at each steady state. You need to check the system at each operating point. It may not be unstable at every point. The whole theory about this is nonlinear dynamics and bifurcation etc etc.
It could be (not sure) possible that system is unstable and linearised one is stabel (and vice versa) as linearized system is just an approximation.
If you specify more details abot the problem then it could be helpful. So give more details.

Prashant

### RE: Nonlinear vs linear system

(OP)
Dear Prashant,

Yes, I simulated the nonlinear model via Matlab/Simulink (SimMechanics) and saw that it was nonlinear.
I have now understood the whole story.
Thanks

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