Structural analysis of sensor location for disturbance rejection by measurement feedback

The Disturbance Rejection by Measurement Feedback (DRMF) is a well known problem mixing control and estimation aspect, whose resolution relies on a good knowledge of the system structural properties. The solvability conditions are highly dependent on the sensor locations. In this paper we analyze the sensor location issues for the DRMF of structured systems which are a large class of parameter dependent linear systems. The sensor location for this problem is already solved in the literature for the case of systems with a single disturbance. It turns out that the sensors must measure state variables in regions close enough to the action of the disturbance. In the multiple disturbance case, the problem is much more complex; some close measurements may be useless while others more distant are useful. In this paper we solve the multiple disturbance case and provide with a full characterization of the sensor location for DRMF. Sets of state variables that are not useful to measure because they never belong to a minimal sensor solution as well as sets of state variables that belong to minimal solutions are determined easily on the system associated graph.