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Paper details
Number 4 - December 1997
Volume 7 - 1997
nD control systems in a practical sense
Li Xu, Osami Saito, Kenichi Abe
Abstract
In view of the features of practical nD signals and systems, this paper presents a comprehensive treatment on some theoretical and methodological results and possible applications for the control of nD systems in the practical sense that the input and output signals of the systems are unbounded in, at most, one dimension. Recent results on the basic properties and control problems for the case under consideration such as practical BIBO and internal stabilities, practical controllability and observability, feedback practical stabilization by both the algebraic and the state-space method, and the relation between the two methods will be summarized. Further contributions to the practical tracking problem and its applications will also be developed. The results obtained make it clear that the nD control problems considered in the practical sense can be essentially reduced to the corresponding ID problems, and thus can be solved, when compared with the conventional nD system theory, under less restrictive stability conditions and by much simpler ID methods. In particular, it is shown that the proposed method for 2D practical tracking control in fact provides a general design approach for a class of iterative learning control systems and linear multipass processes. Therefore, the presented control theory for nD systems in the practical sense is of significance not only from the point of view of practical applications of nnD system theory, but also from that of control of such iterative systems.
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