On the Popov criterion

It is reasonable to expect that the ‘ Popov criterion ’ for the stability of systems containing an arbitrary, finite number of non-linear feedback elements can be improved when the hypothetical transfer function considered in the ‘ Popov criterion ’ is assumed to satisfy meaningful requirements. This paper shows that when certain auxiliary conditions are met, the stability criterion of the multivariable control system containing many nonlinear feedback elements reduces to the original Popov criterion for single loop systems.