A vector Small-Gain Theorem for general nonlinear control systems

A new small-gain theorem is presented for general nonlinear control systems described either by ordinary differential equations or by retarded functional differential equations. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability results. It is shown that the proposed approach recovers several recent results as special instances and is extendible to other important classes of control systems.