Problemi di stabilizzazione ed ottimizzazione con feedback discontinui per sistemi di controllo

The note is concerned with ``patchy vector fields'', a class of discontinuous, piecewise smooth vector fields that were introduced to study feedback stabilization problems. Such vector fields result to be quite appropriate also for addressing the problem of constructing nearly-optimal feedbacks for general optimization problems. Definitions and basic properties of patchy vector fields are illustrated, together with application to control problems.