Sensor location and classification for disturbance rejection by measurement feedback
Résumé
This paper deals with the Disturbance Rejection by Measurement Feedback (DRMF) problem in a structural framework. A new structural necessary and sufficient condition for the solvability of this problem is stated. This condition gives a new insight into the problem and allows to tackle the sensor network design, in particular, sensor location and sensor classification leading to the solvability of the DRMF problem. In the single disturbance case, we characterize in a simple way from the graph associated with the system the sensors which are essential, \emph{i.e.} which failure leads to solvability loss and those which are useless for solvability purpose. In the general case, a lower bound on the number of sensors to be implemented is given. Then we prove that measuring state variables outside a given subset is useless and that measuring state variables sufficiently close to the disturbances in the system associated graph is sufficient for solving the DRMF problem.