This paper addresses the consensus problem of second-order nonlinear multi-agent systems (MASs) under directed topologies using nonsingular terminal sliding mode (NTSM) control. The proposed finite-time and fixed-time consensus algorithms guarantee that the MAS attains the NTSM surface in finite/fixed time and stabilizes on it, thereby achieving the corresponding consensus tracking. Theoretical analysis reveals that the convergence time of finite-time consensus depends on the system’s initial states, whereas fixed-time consensus is independent of initial conditions but highly influenced by control parameters. Rigorous proofs are provided using graph theory and Lyapunov stability theory, and numerical simulations validate the theoretical findings.
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