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In this paper, we consider composite networks formed from the Kroneckerproduct of smaller networks. We find the observability and controllabilityproperties of the product network from those of its constituent smallernetworks. The overall network is modeled as a Linear-Structure-Invariant (LSI)dynamical system where the underlying matrices have a fixed zero/non-zerostructure but the non-zero elements are potentially time-varying. This approachallows to model the system parameters as free variables whose values may onlybe known within a certain tolerance. We particularly look for minimalsufficient conditions on the observability and controllability of the compositenetwork, which have a direct application in distributed estimation and in thedesign of networked control systems. The methodology in this paper is based onthe structured systems analysis and graph theory, and therefore, the resultsare generic, i.e., they apply to almost all non-zero choices of freeparameters. We show the controllability/observability results for compositeproduct networks resulting from full structural-rank systems and self-dampednetworks. We provide an illustrative example of estimation based on Kalmanfiltering over a composite network to verify our results.

Minimal Sufficient Conditions for Structural Observability/Controllability of Composite Networks via Kronecker Product