Discrete‐time systems with slope restricted nonlinearities: Zames–Falb multiplier analysis using external positivity. (24th January 2021)

• Record Type: Journal Article
• Authors: Turner, Matthew C.; Drummond, Ross
• Other Names: Wan Yan guestEditor.; Yang Tao guestEditor.; Yuan Ye guestEditor.; Lewis Frank L. guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 6(2021)
• Page Start: 2255
• Page End: 2273
• Publication Date: 2021-01-24
• Subjects: absolute stability -- integral quadratic constraints -- robust control; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5391
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: 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.