Controllability and stabilization for linear systems of algebraic and differential equations

In this paper, we study several reachability and controllability definitions for linear, autonomous systems of degenerate ordinary differential equations. We try to identify the most interesting among them; we prove the connections with stabilizability and full stabilizability properties of the systems, which are also studied. In particular, we show the connection of the stabilizability property with the existence of special solutions of a suitable version of the Riccati equation.This paper was written under the auspices of GNAFA-CNR (Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni, Consiglio Nazionale delle Ricerche), Rome Italy.