Linearizazion second order System

[edge]

Hi all,

I'm a new user , I'm Italian so sorry for my bad english.

 

My problem is that :

 

I have this second order system non linear:

[latex]x(k+1) = a \cdot x(k) + b \cdot \sqrt{(x(k-1))} + c \cdot u(k)[/latex]

 

I would like to have a new system that is the linearizazion of my one.

I know how to linearize a first order system, but in this case how can i do ?

 

Thanks

Edited May 25, 2013 by edge

[studiot]

Over what range of x do you wish to work, and is u(k) a linear function of k or what?

 

The first term on the right is linear.

 

The second term requires a range so that you can replace the square root by a linear funtion of x(k_n)

 

The u(k) requires defining so that its linearisation can be evaluated.

Edited May 25, 2013 by studiot

[edge]

I'm sorry . My system has changed and now I try to be more precise.

y(k+1) = a*y(k)*(n(k))/L + b*u(k+1);

 

Where y(k) is th output of my system, n(k) is an input, u(k) too.

Best Regards