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Stability of Linear Time-Invariant Systems

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The stability of a single-input, single-output, singleloop, linear, time-invariant system is related to the properties of its open-loop gain. The impulse response of the open-loop system may be of the formg(t) = r + g_{a}(t) + sum_{i=0}^{infty} g_{i} delta (t - t_{i})whereris a nonnegative constant,g_{a}is integrable on[0, infty), andsum_{i=0}^{infty} |g_{i}|<infty. If the Nyquist diagram of the open-loop gain does not go through nor encircle the critical point, then the closed-loop system is inputoutput stable, in the several meanings explained in the paper.

Published in:

Circuit Theory, IEEE Transactions on  (Volume:15 ,  Issue: 3 )

Date of Publication:

Sep 1968

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