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Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 250 (10 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
Minimal Realization in the Max Algebra is an Extended Linear Complementarity Problem
 SYSTEMS & CONTROL LETTERS
, 1993
"... In this paper 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 inpu ..."
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Cited by 29 (26 self)
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In this paper 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 maxlinear discrete event system.
The characteristic equation and minimal state space realization of SISO systems in the max algebra
, 1994
"... this report, please use the following reference instead: ..."
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Cited by 7 (6 self)
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this report, please use the following reference instead:
The QR decomposition and the singular value decomposition in the symmetrized maxplus algebra
, 1998
"... ..."
Minimal state space realization of SISO systems in the max algebra
, 1993
"... First we determine necessary and for some cases also sufficient conditions for a polynomial to be the characteristic polynomial of a matrix with elements in Rmax. Then we indicate how to construct a matrix such that its characteristic polynomial is equal to a given monic polynomial in Smax , the ext ..."
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Cited by 3 (3 self)
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First we determine necessary and for some cases also sufficient conditions for a polynomial to be the characteristic polynomial of a matrix with elements in Rmax. Then we indicate how to construct a matrix such that its characteristic polynomial is equal to a given monic polynomial in Smax , the extension of Rmax . Next we use these results to develop a procedure to nd the minimal state space realization of a single input single output (SISO) discrete event system, given its Markov parameters.
Minimal Realizations and State Space Transformations in the Symmetrized MaxAlgebra
, 1998
"... Similarity transformations between two different minimal realizations of a given impulse response of a Discrete Event System are discussed. In the symmetrized maxalgebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response a ..."
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Cited by 2 (0 self)
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Similarity transformations between two different minimal realizations of a given impulse response of a Discrete Event System are discussed. In the symmetrized maxalgebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response and a minimal realization of the same impulse response in a standard form. It is conjectured that a more general result holds which gives a transformation matrix between any two minimal realizations of an impulse response. We will illustrate the difficulties encountered when trying to prove this conjecture.