Finding the function of the supremum

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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.

Accepted Answer

Torsten
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
  7 Comments
Walter Roberson
Walter Roberson on 1 Oct 2022
or consider a Gaussian. The sup is at the peak but the limit at infinity is 0.

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More Answers (2)

Sam Chak
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
  1 Comment
Aysel Alimirzayeva
Aysel Alimirzayeva on 30 Sep 2022
@Sam Chak The information you gave me was very useful. Thank you very much.

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Osmar Tormena Júnior
Osmar Tormena Júnior on 30 Mar 2023
Following p-norm definition, the supremum may be defined as:
Which may be computed by
Bx = limit((int(abs(x)^p, dummy, -Inf, Inf))^(1/p), p, Inf);
for a suitable dummy integration variable.
Alas, the solution appears to be beyond the Toolbox analytical capability. It fails for common signals like constants, unit step, etc. Even when it doesn't fail, it does not return the final result — although it still works with isfinite() function to test if . Really, the only kind of signal this has worked out is a gaussian.

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