Structural Analysis of the Partial State and Input Observability for Structured Linear Systems: Application to Distributed Systems

This paper deals with the partial state and input observability analysis for structured linear systems with an application to distributed systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. More precisely, we express, in simple graphic terms, necessary and sufficient conditions for the strong observability of a state or an input component. These results are then directly applied to study the observability of a distributed system in some different configurations. In fact, we define two configurations called decentralized interconnected observation scheme and decentralized autonomous observation scheme, for which we check whether or not any given part of the states or the inputs of a considered subsystem is strongly observable. All the provided conditions are easy to verify because they are based on comparison of integers and on finding paths in a digraph.