RELAXED CHARACTERIZATIONS OF SMOOTH PATCHY CONTROL LYAPUNOV FUNCTIONS

A smooth patchy control Lyapunov function for a nonlinear control system consists of an ordered family of smooth local control Lyapunov functions, whose open domains form a locally finite cover of the state space of the system, and which satisfy a certain arrangement property. In contrast to (Goebel et al., IEEE CDC, 2006), on each intersection of the domains, we do not impose a decrease condition of the local control Lyapunov functions when the index increases. We show a construction, based on such a patchy control Lyapunov function, of a stabilizing hybrid feedback that is robust to measurement noise. Copyrighte 2007 IFAC