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Finite poles and zeros of linear systems: An intrinsic approach. (English) Zbl 1034.93009
This paper follows the intrinsic approach, considering linear systems as modules, as developed by M. Fliess [Int. J. Control 49, 1989-1999 (1990; Zbl 0684.93001)]. The aim is to define and study various kinds of zeros and poles in this module theoretic setting. These include Smith zeros, structural indices, system poles, controllable poles, observable poles, transmission poles, input-decoupling zeros, output-decoupling zeros, input-output-decoupling zeros, hidden modes, invariant zeros, transmission zeros, blocking zeros and system zeros. New relationships between some of these poles and zeros emerge, while other known ones are confirmed. The authors also show how the structural indices of an input-output-decoupling zero can be calculated. The module-theoretic setting also proves convenient for solving the problem of choosing suitable input variables of a linear system where they are not a priori distinguished. Various examples highlight the text.

MSC:
93B25 Algebraic methods
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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