In this chapter, we formulate our main problem and discuss some necessary mathematical concepts related to feedback control design for nonlinear systems under sample-data output measurements. Then we present a theoretical analysis of an extended version of the invariant ellipsoid method. Then two feedbacks are analyzed: a linear feedback proportional to the current state estimate obtained by a Luenberger-type estimator; anda full-order linear dynamic controller governed by a linear ordinary differential equation with available sample data as input. Then we construct a minimal attractive ellipsoid that guarantees stability of the system in a practical sense by varying all parameters of the suggested feedbacks. The associated numerical techniques are also presented. An implementable algorithm for the constructive treatment of the robust control design problem is proposed.