Sensor location for the disturbance rejection by measurement feedback problem

In this paper we study the sensor location problem for the Disturbance Rejection by Measurement Feedback (DRMF). We are concerned with linear systems which are affected by unmeasurable disturbances and we look for a measurement feedback which rejects these disturbances. We present new understandings to the DRMF problem described in the context of linear structured systems. In the case where there exists a single disturbance, we prove that it is necessary and sufficient to have a measurement inside a disc of the system associated graph. In the general case, we give the minimal number of sensors to be implemented for solving the DRMF problem. When we have q disturbances and when the problem is solvable with a given sensor set, we show that the problem is solvable with at most q sensors of the previous sensor set. Finally, we provide with a constructive sensor network configuration which solves the DRMF problem. The results are illustrated on graphs of simple systems. Copyright © IFAC 2010