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Linearizing ordinary differential equations

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thavamaran

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Hi guys, im trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I cant get a proper reference on this state-space model.

Attached is the non-linear ode, the partial derivative of the non-linear ode and the state-space model of jacobian matrix.

Can someone enhance or explain how they got the state-space model as the transformation, is it a fix formulation. Sorry for asking this way cause I cant find any books or reference referring or explaining this. Please help me! thanks!
 

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I think state space method is the easiest one and it is discussed in Ogata book about Linear control systems Desidn
 

If this is a physics (engineering?) problem any attempt at linearizing needs to be driven by the physics (engineering) of the system....so until you explain that I don't think anyone can help.
rt
 

It easy in anyway you look at it. I will give three steps
1. Identify how many variables you have in the whole system
2. If 1, use Taylor series expansion of 1 variable of order1. If 2 or more use Taylor series expansion for multiple variables of order1.
3. identify the normal operating variable i.e. X=X(0)+x s.t dX/dt =dx/dt.
after this three steps u will have your equations in the linearise version
 

Well, I think if you want to know more about state space you would like to see this page:

State space (controls) - Wikipedia, the free encyclopedia

and as you may have remarked linearization is needed for this model to work...
so you might find that using taylor series before moving to the state space model very useful.
 

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