High-order Zames-Falb multiplier analysis using linear matrix inequalities

This paper proposes an algorithm for stability analysis of systems containing slope-restricted nonlinearities using high-order Zames-Falb multipliers. The main innovation in this paper is the use of a new congruence transformation which enables multipliers of twice the order of the linear part of the system to be used in a linear-matrix-inequality (LMI) framework for stability analysis. Although the use of such high-order multipliers increases computational requirements, various numerical examples show that the resulting stability bounds are sometimes less conservative than using other similar approaches.