Cartesian Products of Z-matrix Networks: Factorization and Interval Analysis∗
نویسندگان
چکیده
This paper examines the relationship between the dynamics of large networks and of their smaller factor-networks (factors) obtained through the factorization of the network's graph representation. We speci cally examine dynamics of networks which have Z-matrix state matrices. We perform a Cartesian product decomposition on its network structure producing factors which also have Z-matrix dynamics. A factorization lemma is presented that represents the trajectories of the large network in terms of the factors' trajectories. An interval matrix lemma provides families of network dynamics whose trajectories are bounded by the interval bounds' factors' trajectories.
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