Discrete-time systems with slope restricted nonlinearities: Zames-Falb multiplier analysis using external positivity

This article exploits positive systems theory in the search for Zames-Falb multipliers for the analysis of discrete-time Lurie systems, where the nonlinearity is assumed to be slope-restricted. Although a similar problem has been tackled in a continuous time context, the results in discrete-time take a different form and require a somewhat different approach to overcome certain technical problems. The work has two compelling features: (i) the arising algorithms are completely convex; and (ii) numerical results compare well with the state-of-the-art in some cases, providing the least conservative result in one instance.