Integral action for uncertain switched affine systems with application to DC/DC converters

The paper addresses the problem of designing a stabilizing control for switched affine systems in presence of a model uncertainties. We formulate the problem both in the case where the set of affine subsystems is finite and in the case where the set of affine subsystems is not finite but given by a convex polytope, i.e., the convex hull of finitely many affine subsystems. The main contribution of this work shows how to include in the design an integral action and how a switched control with a global asymptotic stability property can be deduced. It is proved that the design procedure ensures zero steady state error on the controlled output when the discrepancy between the model and the real system is bounded. Finally, a $\mathrm {D}\mathrm {C}/\mathrm {D}\mathrm {C}$ Flyback converter is considered to illustrate the effectiveness of the proposed method. We also show that the proposed strategy allows to cancel the steady state error in mean value when the continuous time feedback is sampled.