Stabilization of switched affine systems: An application to the buck-boost converter

In this paper we extend a technique developed to design a feedback stabilizing control law for autonomous switched systems all modes of which are unstable. More specifically, we extend the switching table procedure to the class of affine switched systems, the dynamics of which either do not have an equilibrium point or, if they do, it is not common. This method is then applied to the DC-DC buck-boost converter. The design of the control law is based on dynamic programming and it results in a partition of the state space into switching look-up tables. A comparison with a Lyapunov based technique is also discussed.