Abstract
Repetitive processes are a distinct class of two-dimensional (2D) systems (i.e., information propagation in two independent directions occurs) of both systems theoretic and applications interest. In particular, a repetitive process makes a series of sweeps or passes through dynamics defined on a finite duration. At the end of each pass, the process returns to the starting point and the next pass begins. The critical feature is that the output on the previous pass acts as a forcing function on, and hence contributes to, the current pass output. There has been a considerable volume of profitable work on the development of a control theory for such processes but more recent applications areas require models with terms that cannot be controlled using existing results. This paper develops substantial new results on a model which contains some of these missing terms in the form of stability analysis and control law design algorithms. The starting point is an abstract model in a Banach space description where the pass-to-pass coupling is defined by a bounded linear operator mapping this space into itself and the analysis is extended to obtain the first results on robust control.
This work has been partially supported by the Ministry of Science and Higher Education in Poland under the project N N514 293235.
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Communicated by J.A. Ball.
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Cichy, B., Gałkowski, K., Rogers, E. (2010). Control Laws for Discrete Linear Repetitive Processes with Smoothed Previous Pass Dynamics. In: Ball, J.A., Bolotnikov, V., Rodman, L., Spitkovsky, I.M., Helton, J.W. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 203. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0161-0_8
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DOI: https://doi.org/10.1007/978-3-0346-0161-0_8
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