A POLYNOMIAL MATRIX-THEORY FOR A CERTAIN CLASS OF 2-DIMENSIONAL LINEAR-SYSTEMS

Repetitive, or multipass, processes are a class of 2D systems characte rized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. The unique co ntrol problem arises from the explicit interaction between successive pass profiles, which can lead to oscillations in the output sequence t hat increase in amplitude in the pass to pass direction. Precious work has developed a 2D transfer function matrix representation for one li near subclass of practical interest. This article uses this representa tion to develop major new results on a polynomial matrix-based interpr etation of their fundamental dynamic behavior. A key feature here (in comparison to the extremely well-developed standard linear systems cas e) is the need to take due account of difficulties arising from the co mplexity of the underlying polynomial ring structure.