The disturbance rejection by measurement feedback problem revisited

In this paper, we revisit the disturbance rejection by measurement feedback (DRMF) problem in a structural framework. We prove that the study of this problem can be restricted to a subset of the state space and that the DRMF problem reduces to an unknown input observer problem on this subset. This result allows to explain why we need to estimate a sufficient number of state variables and early enough in order to estimate the disturbance effect and compensate for it via the control input. We give the minimal number of sensors to be implemented for solving the DRMF problem and prove that measuring in some parts of the state space is useless. Our analysis is performed in the context of structured systems which represent a large class of parameter dependent linear systems.