This seminar is entirely devoted to present and discuss new perspectives on sampled-data control systems that follow from Bellman’s Principle of Optimality. The main goal is to reproduce the classical results in the framework of linearmatrix inequalities (LMIs). Stability characterization and performance-based H-2 and H-infinity norms determination will be discussed. Robust stability and performance analysis for systems with uncertain parameters belonging to polytopic domains will be addressed. Our intention is to put in evidence some important aspects associated to state feedback and dynamic output feedback sampled-data control design. Academical examples will be used for illustration.