A polynomial matrix theory for a certain class of two-dimensional linear systems Original Research Article

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