Filtered Lyapunov functions and their applications in the stability analysis of nonlinear systems

— In this paper we introduce a new type of Lyapunov functions in a general framework particularly suitable for the analysis of systems with noise and uncertainty. These Lyapunov functions may depend on parameters possibly satisfying differential equations or inequalities. The main differences with respect to classical Lyapunov functions and classical tools for the design of composite Lyapunov functions are discussed through examples. A design tool for the design of composite filtered Lyapunov functions is given and examples show improvements over existing literature.