Stability of control systems with multiple nonlinearities

This paper generalizes the Popov criterion for the stability of a system containing a simple memoryless nonlinearity to the case of a system containing an arbitrary number of memoryless nonlinearities. In stating the problem formally, we point out two apparently distinct occurrences of nonlinearities which are really not different, so that both are in the ambit of the problem considered. The main result is established, with an application to deriving a subsidiary result, already discovered by other techniques, on the stability of second-order nonlinear systems.