Combinatorial dynamical system theory: general framework and controllability criteria
K Murota - Discrete Applied Mathematics, 1988 - Elsevier
Discrete Applied Mathematics, 1988•Elsevier
A combinatorial analogue of the dynamical system theory is developed in a matroid-
theoretic framework. The combinatorial dynamical system is described by a combinatorial
analogue of the state-space equation x k+ 1= Ax k+ Bu k; the matrices A and B are to be
replaced by bimatroids (or linking systems). Related concepts such as controllability are
defined and their fundamental properties are investigated. In particular, a sequence of
matroids {R k} determined by a “stationary iteration” R k+ 1= A* R k∨ N is considered …
theoretic framework. The combinatorial dynamical system is described by a combinatorial
analogue of the state-space equation x k+ 1= Ax k+ Bu k; the matrices A and B are to be
replaced by bimatroids (or linking systems). Related concepts such as controllability are
defined and their fundamental properties are investigated. In particular, a sequence of
matroids {R k} determined by a “stationary iteration” R k+ 1= A* R k∨ N is considered …
Abstract
A combinatorial analogue of the dynamical system theory is developed in a matroid-theoretic framework. The combinatorial dynamical system is described by a combinatorial analogue of the state-space equation xk + 1 =Axk + Buk; the matrices A and B are to be replaced by bimatroids (or linking systems). Related concepts such as controllability are defined and their fundamental properties are investigated. In particular, a sequence of matroids {Rk} determined by a “stationary iteration” Rk + 1 =A *Rk∨N is considered, whereA * Rk is the matroid induced fromRk by a bimatroidA, andN is a matroid.
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