are these stabability conditions the same?

From: kiki (lunaliu3_at_yahoo.com)
Date: 12/28/04 

Date: Mon, 27 Dec 2004 17:16:06 -0800

Hi all,

I understood the two stability conditions:

One is BIBO criteria in Fourier analysis... it says that if the impulse
response is not absolute integrable, i.e. if Integrate(|h(t)|, t from -inf
to inf)=inf then the system is not BIBO stable...

>From this criteria, an ideal low pass filter is not BIBO stable, since its
impulse response is "sinc" function, which can be proved to have
Integrate(|sinc(t)|, t from -inf to inf)=inf...

Another criteria is the negative real part of the poles criteria in Laplace
analysis, which says that for a system to be stable, its poles should have
negative real parts...(on the left plane on the complex s-domain)...

According to this criteria, the Laplace transform of the impulse function
sinc(t) is:

-----------------------------------------------
>> syms t s
>> laplace(sin(pi*t)/(pi*t))

ans =

1/pi*atan(pi/s)
-----------------------------------------------

But it has no pole at all... so sinc(t) is a stable system according to this
Laplace analysis.

Isn't this strange? Did I miss anything?

Can anybody throw me some lights? And talk something about the relationships
of these various conditions for stabality systems?

Thanks a lot

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