Global stability of two linearly interconnected nonlinear systems

Simple and easy to use conditions are developed which guarantee global stability of two linearly interconnected nonlinear systems. The conditions consist of two scalar frequency response conditions of Popov type on the linear dynamical subsystems and inequalities involving the sector bounds and parameters in the problem; the inequalities have a simple graphical interpretation in terms of the product of the interconnection coefficients. Examples with particular numerical values are presented to illustrate application of the results.