Stability of Linear Time-Invariant Systems

Abstract

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.