To determine whether the system is stable.

I have writen the code to determine the stability of a system. However, the result keeps saying that 'System is not stable' even if I checked the value of pm in workspace and it shows that pm equals to 1, which means that the system is marginally stable. What's wrong with it?

b = [1 0 0 -1 0];
a = [1 0 0 0 -1];
zplane(b,a)
p = roots(a);
pm = abs(p);
if max(pm) <= 1
    disp('System is stable');
else
    disp('System is not stable');
end
end

Answer 1

[Star Strider]

Welcome to the wonderful world of floating-point approximation error!

See ‘Check’ and ‘Check_max’ for an illustration of the probllem:

format long                                         % View Full Precision Results
b = [1 0 0 -1 0];
a = [1 0 0 0 -1];
zplane(b,a)

p = roots(a)

p = 
 -1.000000000000000 + 0.000000000000000i
  0.000000000000000 + 1.000000000000000i
  0.000000000000000 - 1.000000000000000i
  1.000000000000000 + 0.000000000000000i

pm = abs(p)

pm = 4×1

1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000

Check = pm-1

Check = 4×1

1.0e+-15 * 0.444089209850063 -0.444089209850063 -0.444089209850063 -0.111022302462516

Check_max = max(pm)-1

Check_max = 
     4.440892098500626e-16

if max(pm) <= 1
    disp('System is stable');
else
    disp('System is not stable');
end

System is not stable

% end

See the documentation on Floating-Point Numbers for an extended discussion on this topic.

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