Predefined-time stability for a class of dynamical systems and its application on the consensus control for nonlinear multi-agent systems

Abstract

This paper focuses primarily on the predefined-time stability for a class of fixed-time stable systems, with the least upper bound of the settling time as an explicit parameter. It is mathematically proved that the systems under consideration herein can reach stability within any preassigned time, rather than the overestimation of convergence time found in previous fixed-time stability. Comparisons show that our studied system is more general than some classical ones, and that many existing results can be derived. As an application of the exposed stability analysis, static and adaptive predefined-time control algorithms are designed to study the average consensus problem for nonlinear leaderless multi-agent systems. Particularly, the adaptive control protocol guarantees predefined-time consensus without requiring the global topology information of the systems under consideration. Numerical simulations are provided throughout to support our theoretical results.