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On the stability of linear repetitive processes described by a delay-difference equation

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2 Author(s)
Rogers, E. ; Sch. of Electron. & Comput. Sci., Univ. of Southampton, UK ; Owens, D.H.

This paper considers linear repetitive processes which are a distinct class of two-dimensional 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.

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Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:51 ,  Issue: 7 )