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This paper aims at the study of controllability properties and inducedcontrollability metrics on complex networks governed by a class of (discretetime) linear decision processes with mul-tiplicative noise. The dynamics aregiven by a couple consisting of a Markov trend and a linear decision processfor which both the "deterministic" and the noise components rely ontrend-dependent matrices. We discuss approximate, approximate null and exactnull-controllability. Several examples are given to illustrate the linksbetween these concepts and to compare our results with their continuous-timecounterpart (given in [16]). We introduce a class of backward stochasticRiccati difference schemes (BSRDS) and study their solvability for particularframeworks. These BSRDS allow one to introduce Gramian-like controllabilitymetrics. As application of these metrics, we propose a minimalintervention-targeted reduction in the study of gene networks.

Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise