Inverse Laplace Transform -Exponential

Hello All: Does anyone know of a matlab code to obtain the inverse Laplace transform of an exponential? or hints

Answer 1

[Walter Roberson]

There does not appear to be any general form for all exponentials, but some exponential forms have simple transforms.

Perhaps you have a specific form you would like to consider?

[Melany]

Walter:

It is pretty general and pretty much the addition of two exponentials

A * exp(-lambda1 * x) + B * exp(-lambda2 * x)

any hints?

[Walter Roberson]

Under the assumptions that all the variables are real, and that lambda1 and lambda2 are positive (so you have a negative exponential), then the form for that is

A * Dirac(t-lambda1) + B * Dirac(t-lambda2)

However if lambda1 or lambda2 are complex or are negative, then you have a problem.

[Giuseppe Maria D'Aucelli]

This actually solved my problem. In other words, assuming the "delay" parameter to be positive allows flawless inverse Laplace transform computation. Example below:

% Time and delay parameters
syms t, td real
% Laplace complex variable
syms s

F = exp(- td*s);
f = ilaplace(F)

Gives an unusable result:

f =
ilaplace(exp(-s*td), s, t)

But the explicit assumption of positive delay makes the trick and helps Matlab find the right solution. So, if the assumption is added:

assume(td > 0)

The output will be the expected one:

f =
dirac(t - td)

And this worked for me in a much more complex transfer function.

Answer 2

[MANOHAR POKA]

Find the inverse Laplace transform of

F(s)=(100*(s+3))/(s+1)*(s+2)*(s^2+2*s+5)

[Walter Roberson]

ilaplace((100*(s+3))/(s+1)*(s+2)*(s^2+2*s+5))