Infinite gain margin, contraction and optimality: An LMI-based design. (November 2022)

• Record Type: Journal Article
• Authors: Giaccagli, Mattia; Andrieu, Vincent; Tarbouriech, Sophie; Astolfi, Daniele
• Is Part Of: European journal of control. Volume 68(2022)
• Publication Date: 2022-11
• Subjects: Nonlinear systems -- Incremental stability -- Contraction -- Linear matrix inequalities -- Infinite gain margin -- Optimality; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2022.100685
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: In this paper we focus on nonlinear systems composed by a linear term plus a nonlinearity satisfying a monotonic or a sector bound condition. We present sufficient conditions based on LMIs for the design of a feedback control law possessing an infinite gain margin property that makes the closed-loop system to define a contraction. Then, we analyze the connection between infinite gain margin contractive feedbacks and optimization problems by showing how such an infinite gain control design minimizes a given cost function. A practical case of study is given to illustrate our results.