Tractable stability analysis for systems containing repeated scalar slope-restricted nonlinearities

This paper proposes an LMI-based approach for studying the stability of feedback interconnections of a finite dimensional LTI system and a nonlinear element that consists of several identical scalar nonlinearities that have restrictions on their sector and slope. The results are based on the integral quadratic constraint stability analysis framework and other recent results that give a sharp characterisation of stability multipliers for monotone, repeated scalar nonlinearities. Several examples show the effectiveness of the proposed approach; the lack of conservatism in the results is noteworthy. Copyright © 2013 John Wiley & Sons, Ltd.