Why does the RESIDUE function return incorrect results in MATLAB?

Why does the RESIDUE function return incorrect results in MATLAB?

The following code provides unexpected results:

a = 0;

b = 1;

[r,p,k] = residue(a,b)

 r =

      []

 p =

      []

 k =

      1

In this case, k should be ZERO and not 1.

Answer 1

[MathWorks Support Team]

This bug has been fixed for Release 14 SP1 (R14SP1). For previous releases, please read below for any possible workarounds:

This is a bug with the RESIDUE function in MATLAB that our development staff is currently investigating.

If you have The Signal Processing Toolbox, you can use the RESIDUEZ function to work around this issue. There are no other known workarounds at this time.

[Paul]

That's not what the outputs of residue mean nor how partial fraction expansion works. The pole at s = 0 is repeated and residue knows that r(2) applies to the repeated pole

num = 1;
den = [1 0 0];
tf(num,den)

ans =
 
   1
  ---
  s^2
 
Continuous-time transfer function.

[r,p,k] = residue(num,den);
[newnum,newden] = residue(r,p,k);
tf(newnum,newden)

ans =
 
   1
  ---
  s^2
 
Continuous-time transfer function.