On the Generalization of the Multivariable Popov Criterion for Slope-Restricted Nonlinearities

The Popov criterion has proved to be a powerful tool for analyzing the absolute stability of Lur’e systems, where a linear time-invariant system is in feedback interconnection with a nonlinear operator. However, its applicability is limited by the stringent requirements that the linear system is strictly proper and the input of the nonlinear operator has a bounded time derivative. In this paper, we relax these requirements for the Popov stability criterion on MIMO systems with nonrepeated diagonal slope-restricted nonlinearities by demonstrating the phase containment of Popov multipliers within the wellestablished O’Shea-Zames-Falb multipliers.