Control Lyapunov functions and stabilizability of compact sets for hybrid systems

For a class of hybrid systems given in terms of constrained differential and difference equations/inclusions, we define control Lyapunov functions, and study their existence when compact sets are asymptotically stable as well as the stabilizability properties guaranteed when they exist. Recent converse Lyapunov theorems for the class of hybrid systems under study enable us to assert that asymptotic stabilizability of a compact set implies the existence of a smooth control Lyapunov function. When control Lyapunov functions are available, conditions for the existence of continuous state-feedback control laws, both providing practical and global stabilizability properties, are provided.