The paper explains two general and complementary concepts of system design that have direct relevance to the theory and design of control systems: the principle of matching and the method of inequalities. One aim of the paper is to supplement, clarify and unify the ideas and explanations contained in previous publications. To this end, the essential ideas are presented in their simplest forms to make the paper also serve the purposes of an introduction and a review of the field. Another aim is to discuss the effects of the concepts on the foundations of the control theory, without neglecting the practical aspects of design.