Fixed-Time Control Lyapunov Function for Networked Non-Linear Uncertain Systems

This paper introduces a novel tool based on Lyapunov functions, aimed at analyzing the fixed-time property of networked non-linear uncertain systems while incorporating a specifically designed control law. The applicability of this tool is demonstrated by addressing the fixed-time synchronization challenge within non-linear uncertain multi-agent systems (MASs) operating in a leader-following scenario. In this scenario, the desired trajectory stems from a general non-linear system, and a two-part solution is presented. Both segments of the solution leverage the innovative Lyapunov function-based tool. The first component entails a fixed-time non-linear state feedback observer, engineered to estimate the leader system's state within a directed communication network. The second component offers a fixed-time control law, designed to regulate the trajectories of the agents. This paper explores two categories of non-linear agents with first-order and second-order dynamics, taking into account parametric uncertainties.