Analysis of MIMO Lurie Systems with Slope Restricted Nonlinearities Using Concepts of External Positivity

Abstract

This paper revisits the stability analysis problem for feedback interconnections comprising a multivariable linear-time-invariant system and a static slope-restricted nonlinear element. The analysis is based on Zames-Falb multipliers but incorporates aspects of external positivity theory to improve the computational efficiency of the multiplier search. An appealing aspect of the work is that few user choices are required to define the stability conditions, making the algorithm straightforward to use. Some numerical examples taken from the literature illustrate the effectiveness of the approach and its competitiveness with the state-of-the-art.