A family of piecewise affine control Lyapunov functions

Ngoc Anh Nguyen (1, 2, 3) , Sorin Olaru (1, 2, 3)

1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 Université Paris-Saclay

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.

Keywords: Control Lyapunov function; Robust control; Convex lifting

Domains: Engineering Sciences [physics]

Ngoc Anh Nguyen, Sorin Olaru. A family of piecewise affine control Lyapunov functions. Automatica, 2018, 90, pp.212-219. ⟨10.1016/j.automatica.2017.12.052⟩. ⟨hal-01692257⟩