An Introduction to Stability and Stabilization

In this lecture we discuss several de nitions of stability for systems with inputs and for their unforced associated systems. We consider also the stabilization problem, both from the internal and the external point of view. All these properties are characterized in the framework of second Liapunov's method. Although nonlinear systems are the main concern of this lecture, we start by a description of what happens in the linear case. By our exposition, we aim also to demonstrate the opportunity of introducing in the treatment di erential inclusions and methods of nonsmooth analysis.