Re: linear/non-linear system


"VijaKhara" <VijaKhara@xxxxxxxxx> wrote in message
news:1156604500.446483.201560@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
hi all,

1. For a system, if the input function is u1(t), the output is y1(t)
and if the input u2(t) the output y2(t). They ask if this system is
linear or not. I simply look for the transfer function:
H1(s)=Y1(s)/U1(s) and H2(s)=Y2(s)/U2(s). If H1(s)=H2(s) the system is
linear, if not it nonlinear. But I am confused. What if the system is
linear but not time invariant. Does the proof above still work?

2. For my specific case:
u1(t)=tstep(t), y2(t)=(t+1)^3step(t+1).
u2(t)=3(t-1)step(t-1), y2(t)=9step(t).

Step(t) is the step function/

Is there any another simpler way to verify the linearity?


3. In control books, they often use Laplace transform to find the
transfer function. Why don't they use Fourier Transform? For some
problems, I feel FOurier Transform is more convenient because we can
compute the transform in both sides (negative and positive).

Thanks


The simplest engineering explanation of linearity is that if you put two
sine wave in at different frequencies then you get out two sine waves at teh
same frequencies shifted in phase and changed in amplitude. If you get
cross-product terms and other terms then it has non-linearities eg

(AcosW1t+Bcos(W2t))^2 is non -linear - a square law and it has a cross
product term and terms at 2W1 and 2W2.

This is of course superposition in action.
M.



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