ON THE EXISTENCE OF CONTROL LYAPUNOV FUNCTIONS - GENERALIZATIONS OF VIDYASAGAR THEOREM ON NONLINEAR STABILIZATION

In this paper the well-known Vidyasagar's theorem concerning the feedback stabilizability problem for interconnected control systems is generalized. In particular, sufficient conditions are provided for the existence of control Lyapunov functions that, according to the results of Artstein, Sontag, and Tsinias, guarantees asymptotic stabilization by means of a feedback law that is smooth, except possibly at the equilibrium at which it is wished to stabilize the system.