Full-block multipliers for repeated, slope-restricted scalar nonlinearities

This paper provides a comprehensive treatment of full-block multipliers within the integral quadratic constraints framework for stability analysis of feedback systems containing repeated, slope-restricted scalar nonlinearities. We develop a novel stability result that offers more flexibility in its application because it allows for the inclusion of general Popov and Yakubovich criteria in combination with the well-established Circle and Zames-Falb stability tests within integral quadratic constraint theory. A particular focus lies on the formulation of stability criteria in terms of full-block multipliers, some of which are new, and thus typically involve less conservatism than current methods. Furthermore, a new asymptotically exact parametrization of full-block Zames-Falb multipliers is given that allows to exploit the complete potential of this stability test. Copyright (C) 2017 John Wiley & Sons, Ltd.