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

ABSTRACT 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.