Observability analysis and sensor location study for structured linear systems in descriptor form with unknown inputs

This paper deals with the state and input right-hand side observability and the sensor location problem to ensure this property for structured linear systems in the descriptor form. The proposed method 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 underdetermined, overdetermined or square. After defining a bipartite graph which represents such systems, we deduce some graphic necessary and sufficient conditions to achieve the right-hand side observability of the state and the input. Next, we propose a sensor placement procedure to recover this property. More precisely, we provide the minimal number of the sensors required and either their pertinent location or a necessary and sufficient condition to check if a given sensor configuration is adequate or not to ensure state and input right-hand side observability. Our approach uses algorithms with polynomial complexity orders and assumes only the knowledge of the system’s structure and so is suited for large scale systems.