help on linearization / linear approximation

[ktoobi]

i need a help on linearization / linear approximation of the following non-linear system about y(t)=0, u(t)=1 for all t>=0.


y"(t) + y ' (t) + y(t) = u^2(t) -1


1) i already tried to find the state space representation with the following equation

x'(t) = A x(t) + B [u^2(t) -1]
y(t) = C x(t)

2) and i got x(t) = e^(At) x(0) + integral(0.t) of e^(t-T) dT where u(t) =1 and assuems x(0)=0

i need to know whether i am on the right path or not of the solution????

 

[ktoobi]

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.