Stability of linear multipass processes

The recent contribution by Edwards to the stability analysis of multipass 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 multipass stability is proposed and characterised by conditions on the system operator. Application of the results to a cogging process and a class of linear, time-invariant systems indicates that previous results are highly pessimistic. The anomaly is explained in terms of a defined notion of stability along the pass.