On the Search for Equilibrium Points of Switched Affine Systems

Abstract: One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the user must specify one of these equilibrium points to be the goal or reference. This can be a cumbersome task, especially if this goal is partially given or only defined as a set of constraints. To tackle this issue, in this paper we describe algorithms that can determine whether a given goal is an equilibrium point of the system and also jointly search for equilibrium points and design globally stabilizing switching functions.