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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 form g(t) = r + g_{a}(t) + \sum _{i=0}^{\infty } g_{i} \delta (t - t_{i}) where r is a nonnegative constant, g_{a} is integrable on [0, \infty ) , and \sum _{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.

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