This chapter is of a tutorial character. The aim here is to introduce some main concepts and auxiliary facts related to the class of control systems and problems under consideration. Moreover, we also give a first abstract problem formulation in the framework of robust and practically stable control design. Some conventional and advanced results related to ordinary differential equations in the framework of the examined class of dynamical systems are also included. Moreover, we take a quick look at the basic computational tool for our problems, namely, at linear matrix inequality techniques. We focus our attention primarily on motivations of the proposed "attractive ellipsoid" method and illustrate it in some simple situations.