Checking the stability of an LTI system
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How can I check with Simulink whether an LTI system is stable? The transfer function is (1-(a^-1)z^-1)/(1-az^-1), where a is some real number. I need to check which values of "a" make the system stable.
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Rick Rosson
on 18 Jul 2011
The transfer function has a single pole at z = a. To ensure stability, all poles must be located inside the unit circle in the z-plane. Therefore, to ensure stability, you need to ensure only that the magnitude of a is strictly less than 1:
stable = (abs(a) < 1);
if stable
fprintf('The system is stable.\n');
else
fprintf('WARNING: The system is NOT stable.\n');
end
HTH.
Rick
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