Filtered Lyapunov functions and the stabilization of block feedforward systems

In this paper we introduce a generalized class of filtered Lyapunov functions, which are Lyapunov functions with time-varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability and robustness properties of Lyapunov functions. On the other hand, filtered Lyapunov functions can be easily handled to construct composite filtered Lyapunov functions for cascaded systems. Tools for the design of composite filtered Lyapunov functions are given and used to construct globally stabilizing dynamic feedback laws for block-feedforward systems with stabilizable linear approximation.