Nonanticipating Lyapunov Functions for Persistently Excited Nonlinear Systems

Persistently excited nonlinear time-varying systems are considered in this paper. Two new quadratic, time-varying, Lyapunov functions are presented, whose time-varying matrices-solutions to suitable linear time-varying matrix differential equations-are causal (nonanticipating) and, thus, differently from related results in the literature, available at runtime. They allow for directly addressing and successfully achieving further adaptation goals, when uncertain parameters affect the system dynamics.