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

TL;DR

This paper derives minimal conditions for the controllability and observability of composite networks formed via Kronecker products, using structured systems and graph theory, with applications in distributed estimation and control.

Contribution

It provides the first minimal sufficient conditions for controllability and observability of composite networks based on their constituent networks, applicable to structured systems.

Findings

Conditions for controllability/observability in full structural-rank systems

Results for self-damped networks

Verification via Kalman filtering example

Abstract

In this paper, we consider composite networks formed from the Kronecker product of smaller networks. We find the observability and controllability properties of the product network from those of its constituent smaller networks. The overall network is modeled as a Linear-Structure-Invariant (LSI) dynamical system where the underlying matrices have a fixed zero/non-zero structure but the non-zero elements are potentially time-varying. This approach allows to model the system parameters as free variables whose values may only be known within a certain tolerance. We particularly look for minimal sufficient conditions on the observability and controllability of the composite network, which have a direct application in distributed estimation and in the design of networked control systems. The methodology in this paper is based on the structured systems analysis and graph theory, and therefore, the results are generic, i.e., they apply to almost all non-zero choices of free parameters. We show the controllability/observability results for composite product networks resulting from full structural-rank systems and self-damped networks. We provide an illustrative example of estimation based on Kalman filtering over a composite network to verify our results.