Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 367526
Title Linear systems theory revisited
Author(s) Willigenburg, L.G. van; Koning, W.L. de
Source Automatica 44 (2008)7. - ISSN 0005-1098 - p. 1686 - 1696.
DOI https://doi.org/10.1016/j.automatica.2007.10.021
Department(s) Systems and Control Group
PE&RC
Publication type Refereed Article in a scientific journal
Publication year 2008
Keyword(s) discrete-time-systems - weighting patterns - controllability - realization
Abstract This paper investigates and clarifies how different definitions of reachability, observability, controllability, reconstructability and minimality that appear in the control literature, may be equivalent or different, depending on the type of linear system. The differences are caused by (1) whether or not the linear system has state dimensions that vary with time (2) bounds on the time axis of the linear system (3) whether or not the initial state is non-zero and (4) whether or not the system is time invariant. Also (5) time-reversibility of systems plays a role. Discrete-time linear strictly proper systems are considered. A recently published result is used to argue that all the results carry over to continuous time. Out of the investigation two types of definitions emerge. One type applies naturally to systems with constant dimensions while the other applies naturally to systems with variable dimensions. This paper reveals that time-varying (state) dimensions that are allowed to be zero are necessary to obtain equivalence between minimality and (weak) reachability together with observability at the systems level. Besides their theoretical significance the results of this paper are of practical importance for model reduction and control of time-varying discrete-time linear systems because they result in minimal realizations with smaller dimensions that are also computed more easily.
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