Journal Article

Stability theory and performance bounds for a class of two-dimensional linear systems with interpass smoothing effects

ERIC ROGERS and DAVID H. OWENS

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 14, issue 4, pages 415-427
Published in print December 1997 | ISSN: 0265-0754
Published online December 1997 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/14.4.415
Stability theory and performance bounds for a class of two-dimensional linear systems with interpass smoothing effects

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Many physical examples of repetitive, or multipass, processes are subjected to dynamic interaction between successive outputs or pass profiles. This so-called interpass smoothing can severely distort the previous pass profile and therefore must be accounted for in any stability analysis. Failure to do this will, in most cases of practical interest, lead to totally incorrect stability conclusion. In this paper, the total variation of a signal, a well known concept in a number of areas, is used to develop the basis of a rigorous stability theory for one linear subclass where the interpass smoothing is modelled by an integral operator. it is also shown that this theory leads to computable bounds on expected system performance under certain classes of input signals. The key point is that elementary tools of functional analysis (coupled with the total variation of a signal) lead, in contrast to other approaches where only existence-type results can be obtained, to computationally feasible stability tests and performance bounds.

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Subjects: Mathematics

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