Stabilization of nonlinear systems with filtered lyapunov functions and feedback passivation

In this paper a generalized class of filtered Lyapunov functions is introduced, which are Lyapunov functions with time-varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability properties as Lyapunov functions. Tools are given for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally stabilizing dynamic feedback laws for block-feedforward systems with stabilizable linear approximation. © 2012 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.