Minimal Inputs/Outputs for Subsystems in a Networked System

TL;DR

This paper explores minimal input/output configurations for subsystems in networked systems, providing conditions and formulas to ensure overall controllability and observability based on subsystem parameters.

Contribution

It introduces novel sufficient and necessary conditions for controllability and observability that depend only on individual subsystem parameters and their degrees.

Findings

Subsystem controllability and observability are necessary and sufficient for the whole system.

Explicit formulas for minimal inputs/outputs per subsystem are provided.

Both sparse and dense connections can ensure system controllability and observability.

Abstract

Minimal input/output selection is investigated in this paper for each subsystem of a networked system. Some novel sufficient conditions are derived respectively for the controllability and observability of a networked system, as well as some necessary conditions. These conditions only depend separately on parameters of each subsystem and its in/out-degrees. It is proven that in order to be able to construct a controllable/observable networked system, it is necessary and sufficient that each subsystem is controllable/observable. In addition, both sparse and dense subsystem connections are helpful in making the whole system controllable/observable. An explicit formula is given for the smallest number of inputs/outputs for each subsystem required to guarantee controllability/observability of the whole system.