Constructions of strict Lyapunov functions for discrete time and hybrid time-varying systems

Abstract — We announce new methods for explicitly con-structing strict input-to-state stable (ISS) Lyapunov functions for time-varying nonlinear systems. Our constructions are expressed in terms of nonstrict ISS Lyapunov functions which we assume are given. The nonstrict Lyapunov functions can in turn be constructed by known methods for many systems of interest. We also provide a new method for explicitly constructing input-to-output stable (IOS) Lyapunov functions for time-varying systems with outputs. We illustrate our results using a tracking problem for a rotating rigid body. Key Words: Lyapunov functions, time-varying systems with outputs, input-to-state and input-to-output stability