The Stability of Linear Multi-Pass Processes

The recent contribution by Edwards to the stability analysis of multi-pass processes using the familiar inverse-Nyquist method is discussed using the techniques of functional analysis. It is noted that the modelling procedure suggested by Edwards neglects the finite pass length nature of the processes and takes no account of the initial conditions for each pass. A natural and physically meaningful definition of multi-pass stability is proposed and characterized by conditions on the system operator. Application of the results to a cogging process and a class of linear, time-variant system indicates that previous results are highly pessimistic. The anomaly is explained in terms of a defined notion of stability along the pass.