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Abstract: : We demonstrate that the minimal state space realization problem in the max algebra can be transformed into an Extended Linear Complementarity Problem (ELCP). We use an algorithm that finds all solutions of an ELCP to find all equivalent minimal state space realizations of a single input single output (SISO) discrete event system. We also give a geometrical description of the set of all minimal realizations of a SISO max-linear discrete event system. Keywords: discrete event systems, max... (Update)
Context of citations to this paper: More
.... of a class of discrete event systems (DESs) that can be described by a state space model that is linear in the max plus algebra [8, 9]. In this paper we present an overview of this research. Since hybrid systems exhibit characteristics of both CVSs and DESs, this suggests...
...field of mathematical control theory. The problem has given rise to a number of interesting contributions in the last decade, see, e.g. [9, 12, 6, 14, 11]. We give here a proof that the problem is NP hard. For that purpose, let G be a directed graph and let 1, n be the...
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BibTeX entry: (Update)
De Schutter, B. and De Moor, B. 1995. Minimal realization in the max algebra is an extended linear complementarity problem. Systems & Control Letters 25:2, pp. 103-111. http://citeseer.ist.psu.edu/article/deschutter95minimal.html More
@misc{ schutter95minimal,
author = "B. De Schutter and B. De Moor",
title = "Minimal realization in the max algebra is an extended linear complementarity
problem",
text = "De Schutter, B. and De Moor, B. 1995. Minimal realization in the max algebra
is an extended linear complementarity problem. Systems & Control Letters
25:2, pp. 103-111.",
year = "1995",
url = "citeseer.ist.psu.edu/article/deschutter95minimal.html" }
Citations (may not include all citations):267 The Linear Complementarity Problem (context) - Cottle, Pang et al. - 1992
229 Synchronization and Linearity (context) - Baccelli, Cohen et al. - 1992
36 Minimal realization in the max algebra is an extended linear.. - De Schutter, De Moor - 1993
34 The extended linear complementarity problem - De Schutter, De Moor - 1993
31 Th'eorie des Syst`emes Lin'eaires dans les Dioides (context) - Gaubert - 1992
13 an analogy of minimal realizations in conventional and discr.. (context) - Olsder, de Vries - 1987
12 Algebraic realization of discrete dynamic systems (context) - Cuninghame-Green - 1991
10 On minimal realization of SISO DEDS over max algebra (context) - Wang, Xu - 1993
8 The characteristic equation and minimal state space realizat.. - De Schutter, De Moor - 1994
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.esat.kuleuven.ac.be/~deschutt/publications.html): More
On the Sequence of Consecutive Matrix Powers of Boolean.. - De Schutter, De Moor (1998) (Correct)
The Singular Value Decomposition in the Extended Max Algebra - De Schutter, De Moor (1996) (Correct)
Errata for Max-Algebraic System Theory for Discrete Event Systems - De Schutter (1998) (Correct)
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