A family of piecewise affine control Lyapunov functions. (April 2018)

• Record Type: Journal Article
• Authors: Nguyen, Ngoc Anh; Olaru, Sorin
• Is Part Of: Automatica. Volume 90(2018)
• Page Start: 212
• Page End: 219
• Publication Date: 2018-04
• Subjects: Control Lyapunov function -- Robust control -- Convex lifting; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2017.12.052
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper presents a novel method to construct a family of piecewise affine control Lyapunov functions. Unlike most of existing methods which require the contractivity of their domain of definition, the proposed control Lyapunov functions are defined over a so-called N -step controllable set, which is known not to be contractive. Accordingly, a robust control design procedure is presented which only requires solving a linear programming problem at each sampling time. The construction is finally illustrated via a numerical example.