On the Stability of a Class of Distributed, Sampled-Data Nonlinear Systems

Abstract

A frequency domain stability criterion (sufficient condition) for a class of distributed parameter, sampled-data systems containing a memoryless, nonlinear feedback element is presented. This criterion for absolute stability of the class of distributed systems considered here parallels the criterion for lumped systems obtained by Jury and Lee, and it requires that the following relationship be satisfied on the unit circle (|z| = 1 ). Re{W(pj,z) [1 + q(z − 1)]} + 1K − K′|q|2 |(z − 1)W(pj,z)|2 ≥ 0 for all j = 0, 1, 2,.... This sufficient condition is limited to those systems whose dynamics can be described by a transfer function W(pi , z) which is the ratio of the multiple transform of the output to the multiple transform of the input. An example is given to illustrate the applications of the stability criterion.