Stability of a class of systems with multiple nonlinearities

A simple condition for global stability of a class of systems with multiple nonlinearities is established. The systems considered are those that can be formed by interconnecting several subsystems having a single non-linearity. Lyapunov functions of the Lur?? type for the subsystems are constructed from the graphic Popov criterion and the Kalman-Yakubovich Lemma. Using these Lyapunov functions and system parameters it is shown that global stability depends on the definiteness of a matrix. The advantage of this condition is that this matrix can be constructed by an explicit method.