An 2stability criterion with frequency domain interpretation for a class of nonlinear discrete systems

Using the notation and methods of functional analysis, a stability criterion is derived for a class of nonlinear discrete systems. The class of systems investigated consists of a nonlinear static operator satisfying a sector condition, followed by a bounded linear causal operator that satisfies an inner product inequality. A simple graphical means of obtaining stability information similar to the Popov criterion is obtained when the bounded causal linear operator is constrained to be a discrete convolution operator.