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We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring.
Controlled and conditioned invariant subspaces in linear system theory
G. Basile and G. Marro · 1969
Earlier work this paper cites.
Decoupling and pole assignment in linear multivariable systems: a geometric approach
A. S. Morse and W. M. Wonham · 1970
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Status of noninteracting control
A. S. Morse and W. M. Wonham · 1971
Earlier work this paper cites.
Residuation Theory
T. S. Blyth and M. F. Janowitz · 1972
Earlier work this paper cites.
A general separation theorem in extremal algebras
K. Zimmermann · 1977
Earlier work this paper cites.
Minimax Algebra
R. A. Cuninghame-Green · 1979
Earlier work this paper cites.
Controlled invariance in systems over rings
M. L. J. Hautus · 1982
Earlier work this paper cites.
An elimination method for finding all solutions of the system of linear equations over an extremal algebra
P. Butkovič and G. Hegedüs · 1984
Earlier work this paper cites.
A linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing
G. Cohen, D. Dubois, J. P. Quadrat, and M. Viot · 1985
Earlier work this paper cites.
Linear multivariable control: a geometric approach
W. M. Wonham · 1985
Earlier work this paper cites.
Invariance concepts in infinite dimensions
R. F. Curtain · 1986
Earlier work this paper cites.
Algebraic tools for the performance evaluation of discrete event systems
G. Cohen, P. Moller, J. P. Quadrat, and M. Viot · 1989
Earlier work this paper cites.
Controlled and Conditioned Invariants in Linear System Theory
G. Basile and G. Marro · 1991
Earlier work this paper cites.
Synchronization and Linearity
F. Baccelli, G. Cohen, G. J. Olsder, and J. P. Quadrat · 1992
Cited alongside, same era.
Théorie des systèmes linéaires dans les dioïdes
S. Gaubert · 1992
Cited alongside, same era.
Idempotent analysis
V. P. Maslov and S. Samborskiĭ, editors · 1992
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Convex sets in the semimodule of bounded functions
S. N. Samborskiĭ and G. B. Shpiz · 1992
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Problems and results in a geometric approach to the theory of systems over rings
G. Conte and A. M. Perdon · 1994
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The disturbance decoupling problem for systems over a ring
G. Conte and A. M. Perdon · 1995
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Optimal control for ( m a x , + ) (max,+) -linear systems in the presence of disturbances
M. Lhommeau, L. Hardouin, and B. Cottenceau · 2003
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Étude de systèmes à événements discrets dans l’algèbre ( max , + ) (\max,+)
M. Lhommeau · 2003
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Duality and separation theorems in idempotent semimodules
G. Cohen, S. Gaubert, and J. P. Quadrat · 2004
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Interval analysis and dioid: application to robust controller design for timed event graph
M. Lhommeau, L. Hardouin, B. Cottenceau, and L. Jaulin · 2004
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Max-plus convex sets and functions
G. Cohen, S. Gaubert, J. P. Quadrat, and I. Singer · 2005
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Max Plus at work
G. Heidergott, G. J. Olsder, and J. van der Woude · 2006
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V. K. Garg and R. Kumar · 1995
Cited alongside, same era.
Kernels, images and projections in dioids
G. Cohen, S. Gaubert, and J. P. Quadrat · 1996
Cited alongside, same era.
Linear projectors in the max-plus algebra
G. Cohen, S. Gaubert, and J. P. Quadrat · 1997
Cited alongside, same era.
Exotic semirings: Examples and general results
S. Gaubert · 1998
Cited alongside, same era.
Max-plus algebra and system theory: where we are and where to go now
G. Cohen, S. Gaubert, and J. P. Quadrat · 1999
Cited alongside, same era.
Idempotent functional analysis: An algebraic approach
G. L. Litvinov, V. P. Maslov, and G. B. Shpiz · 2001
Cited alongside, same era.
Generators, extremals and bases of max cones
P. Butkovič, H. Schneider, and S. Sergeev · 2007
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The Minkowski theorem for max-plus convex sets
S. Gaubert and R. D. Katz · 2007
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Max-plus (A,B)-invariant spaces and control of timed discrete event systems
R. D. Katz · 2007
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Inferring min and max invariants using max-plus polyhedra
X. Allamigeon, S. Gaubert, and É. Goubault · 2008
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Some remarks on duality over a commutative ring
M. Di Loreto, J. F. Lafay, and J. J. Loiseau · 2008
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The tropical analogue of polar cones
S. Gaubert and R. D. Katz · 2008
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