On the Stability of Linear Repetitive Processes described by a Delay-Difference Equation

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Description/Abstract

This paper considers linear repetitive processes which are a distinct class of 2D continuous-discrete linear systems of both physical and systems theoretic interest. Their essential unique feature is a series of sweeps, termed passes, through a set of dynamics defined over a finite and fixed duration known as the pass length. The result can be oscillations in the output sequence of pass profiles which increase in amplitude in the pass-to-pass direction. This cannot be controlled by existing techniques and instead control must be based on a suitably defined stability theory. In the literature to-date, the development of such a theory has been attempted from two different starting points and in this paper we critically compare these for dynamics defined by a delay-difference equation.