<p>This paper studies an exponential consensus strategy and proves exponential convergence using a variable-gain sampled-data control scheme for nonlinear multi-agent systems. A novel approach is proposed based on the construction of a loop-based discontinuous Lyapunov functional, which guarantees exponential convergence while adaptively regulating the convergence rate. The proposed dynamic gain adjustment enhances stabilization speed and offers significant performance improvements compared to conventional methods. The effectiveness of the discontinuous Lyapunov functional is particularly evident in the context of sampled-data systems, where it results in less conservative stability criteria compared to earlier approaches. To improve computational efficiency, a new integral inequality is derived and redefined to decrease free matrix variables while maintaining its basic framework and adapting it to the particular requirements of our case. Linear matrix inequalities are derived and utilized to calculate the control gain matrices, essential for ensuring system performance. Through numerical examples, the reduced conservatism of the proposed method is demonstrated, particularly with respect to the sampling interval.</p>