2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225917A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state stability results. It is shown that the proposed approach recovers several recent results as special instances and is extendible to several important classes of control systems such as large-scale complex systems, nonlinear sampled-data systems and nonlinear time-delay systems. An application to a biochemical circuit model illustrates the generality and power of the proposed vector small-gain theorem.Submitted to IEEE Transactions on Automatic ControlOptimization and ControlDynamical Systemstext