# Help for Linearization

1. Dec 8, 2009

### ktoobi

urgent help for Linearization

Dear All,

y" (t)+ y'(t)+y(t)=u2(t)-1

Linearize the system about y(t)=0, u(t)=1, for all t>= 0

can we say that this equation is already linear at the given point

which will be y" (t)+ y'(t)+0=1-1 => y" (t) + y'(t)= 0

and no need for linearization.

2. Dec 8, 2009

### trambolin

Re: urgent help for Linearization

No. What you do is only valid for that point (0,1). You need to have a linear system around this point mimicking almost the nonlinear system in a neighborhood hence your input function must be linearized.

3. Dec 8, 2009

### ktoobi

Re: urgent help for Linearization

thank you alot, so how to start solving this system?

do i have to get the state-space representation of this system first? or what?

4. Dec 8, 2009

5. Dec 8, 2009

### ktoobi

Re: urgent help for Linearization

any hint on that?

Last edited: Dec 8, 2009
6. Dec 8, 2009

### trambolin

Re: urgent help for Linearization

$f(x) = x^2$ is your function to be linearized.

7. Dec 8, 2009

### ktoobi

Re: urgent help for Linearization

Thank you alot