Strict Lyapunov Functions for Homogeneous Time-Varying Systems

We provide new criterion and a class of strict Lyapunov functions (SLFs) for time-varying systems (TVSs) with zero homogeneity. The definition of homogeneous auxiliary system is given, where it is assumed that certain homogeneous functions are admitted with their derivatives, in terms of the error systems, bounded by periodic functions. Based on the homogeneous auxiliary system, sufficient conditions of uniform asymptotical stability for TVSs are formulated using the homogeneity framework. Unlike existing results, where non-SLFs or persistence of excitation condition are required, our criterion is greatly relaxed for broad classes of systems. The utility of our result is illustrated by case-study of pendulum stability with quasi-periodical frictions.