Minimal (max,+) Realization of Convex Sequences
SIAM Journal on Control and Optimization
On the boolean minimal realization problem in the max-plus algebra
Systems & Control Letters
Automata, Languages, and Machines
Automata, Languages, and Machines
The set of realizations of a max-plus linear sequence is semi-polyhedral
Journal of Computer and System Sciences
Expository paper: Foundations of system theory: Decomposable systems
Automatica (Journal of IFAC)
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For the theory of realization over semirings, consideration was given to a new problem of generation, that of description of various systems with a given external behavior. A notion was introduced of geometric reduction and geometrically minimal realization based on transformations of arbitrary realizations of the given pulse response into each other, rather than on introducing some invariant of the dimensionality type. This notion was considered for the case of systems over the Boolean semiring: the geometrical reductions were classified, and various properties of the geometrically minimal realizations were studied. Some examples were discussed, as well as one class of non-geometric reductions which enabled us to explain the structure of some sets of geometrically minimal realizations.