Checking the stability of an LTI system

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Anna Eteläaho 2011-7-18

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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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Answer 1

Rick Rosson 2011-7-18

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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