# Finding the function of the supremum

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Aysel Alimirzayeva on 29 Sep 2022
Hello.I have a function I want to calculate its supremum. The function is below.I don't know how to do this in Matlab.Please help me.

Torsten on 29 Sep 2022
Edited: Torsten on 29 Sep 2022
sup-norm is a theoretical concept.
There is no such function in MATLAB to calculate it for a general function.
In the case above you could use
syms t
f = (1-exp(-t))*heaviside(t);
limit(abs(f),t,Inf)
ans =
1
Aysel Alimirzayeva on 2 Oct 2022

Sam Chak on 30 Sep 2022
I'm not sure if the following is what you want. But this 1st-order transfer function (taking the Laplace transform)
produces the same step response as the given Continuous-Time Signal. So the following computes the -Norm of the linear system, instead of the signal.
Also worth checking out these:
t = linspace(0, 10, 1001);
x = 1 - exp(-t);
G = tf(1, [1 1])
G = 1 ----- s + 1 Continuous-time transfer function.
subplot(211)
plot(t, x), grid on, xlabel('t'), title('Continuous-Time Signal')
subplot(212)
step(G, 10), grid on, xlabel('t'), title('Step Response of Transfer Function')
[ninf,fpeak] = norm(G, inf)
ninf = 1
fpeak = 0
Aysel Alimirzayeva on 30 Sep 2022
@Sam Chak The information you gave me was very useful. Thank you very much.

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