A stability criterion for nonuniformly sampled and distributed parameter systems

This paper presents a stability criterion for distributed parameter and uniformly or nonuniformly sampled systems. Specifically, a finite algorithm is presented which tests whether all the zeros of a function of the form $F(s) = \sum_{n=0}^N c_{n}e^{su_n}$ lie within the interior of the left half s-plane. Thus, the algorithm tests the stability of those systems whose system functions are ratios of finite sums of exponentials. Included in such systems are all distributed systems whose components are uniform, lossless transmission lines and all sampled systems with a periodically varying sampling rate.