Characterization of the allowable perturbations for disturbance rejection and data sensitivity

In this paper the problem of disturbance rejection and data sensitivity is studied for the case of linear time invariant systems. Using a proportional state feedback law, the necessary and sufficient conditions for the problem to have a solution are established. The set of all allowable perturbations is explicitly characterized. An independent version of the perturbation special feedback law solving the problem for all allowable perturbations is derived. The necessary and sufficient conditions for disturbance rejection, data sensitivity and BIBO stability are established. A feedback law solving the later problem for all allowable perturbations is also derived.