Constructions of Strict Lyapunov Functions for Homogeneous Time-Varying Systems with Applications in Multi-Agent Systems
Bin Zhang · 2018
We provide a new technique for constructing strict Lyapunov functions (CSLFs) for time-varying systems. 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 time-varying systems are formulated. Unlike classical CSLFs, where non-strict Lyapunov functions or persistency of excitation condition are required, our criterion is greatly relaxed for broad classes of systems. The utility of our result is illustrated through the well-known consensus problem of multi-agent systems.