Observability of structured linear systems in descriptor form: A graph-theoretic approach

This paper deals with the right-hand side observability of structured linear systems in descriptor form. The method we propose is based on a graph-theoretic approach. It is applicable to a large class of descriptor systems including regular and nonregular systems even if they are square, underdetermined or overdetermined. After defining digraphs which represent such systems, we express in graphic terms necessary and sufficient conditions to achieve the observability of the whole or of a given part of the state. These conditions are easy to check because they are based on comparison of integers and on finding edges and subgraphs in a digraph. Therefore, our approach is suited to study large scale and/or uncertain systems.