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To determine whether the system is stable.

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William
William 2021년 9월 21일
답변: Star Strider 2021년 9월 21일
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

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Star Strider
Star Strider 2021년 9월 21일
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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