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

Abstract This paper mainly focuses 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 considered systems can reach stability before any desired time rather than the overestimation of convergence time by previous fixed-time control methods. Furthermore, the comparison shows that our studied systems are more general, and many existing results can be derived. As an application of the exposed stability analysis, a predefined-time control algorithm is designed to study the average consensus problem for nonlinear leader-less multi-agent systems. Numerical simulations are always given to support our theoretical results. Keywords: Predefined-time stability; Fixed-time stable systems; Average consensus; Predefinedtime control algorithm; Multi-agent systems