On the absolute stability of a dynamic system with a nonlinear element function of two state variables

The purpose of this paper is to establish sufficient conditions for absolute stability of a class of control system containing a single nonlinear function of two feedback state variables. In particular, the nonlinearity consists of the product of two linear or non-linear elements, where each element is a function of a different state variable. A frequency-domain stability criterion is obtained which can be verified easily. An example of nonlinear differential equations and an example of a hydraulic system are given to show the practical applications of the results.