Asymptotic stability of continuous-time switched affine systems with unknown equilibrium points^*

This paper deals with switched affine systems control ensuring asymptotic stability of an unknown equilibrium point. More specifically, our study is focused on the class of systems with the affine term depending linearly on an uncertain vector, which can be used to model input and load variations of dc-dc power converters. The main goal is to design a switching function that governs the state trajectories towards an unknown equilibrium point containing in one of its components the desired value specified by the designer. The other components are adapted in real time based on the uncertainty estimation. The design conditions are solved by a two-steps procedure expressed in terms of linear matrix inequalities, and they do not require any stability property of the individual subsystems. The control design of a dc-dc flyback converter is used for illustration and comparison together with an academic example composed of two third order unstable subsystems.