A geometrical stability criterion, similar to the Popov criterion, for time-varying, nonlinear, continuous systems

A stability criterion, applicable in the analysis of a class of single-loop control systems, is derived. The loop of a system from this class of systems consists of a tandem connection of a time-varying gain; a memoryless, time-invariant, nonlinear operator; and an operator which satisfies an inner product inequality. When the operator, satisfying the inner product inequality is a linear, causal, time-invariant, convolution operator, a geometrical interpretation similar to the Popov criterion can be obtained.