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

Abstract

This paper proposes an LMI-based computational framework for studying the stability of feedback interconnections of a finite dimensional linear time invariant system and a nonlinear element which consists of several identical scalar nonlinearities which have restrictions on their sector and slope. The results are based on the IQC stability analysis framework and other recent results which give a sharp characterisation of stability multipliers for monotone, repeated scalar nonlineari-ties. Several examples show the effectiveness of the proposed approach; the lack of conservatism in the results is noteworthy.