Robust sampling-based switching design for piecewise affine systems with application to DC–DC converters

Abstract

The problem of designing the switching rules for piecewise affine systems which satisfy dwell time constraints is studied. With a proposed sampling-based approach which is different from existing traditional switching laws, the system can be updated and switched only at sampling instants. First, a sufficient condition for stability of piecewise linear affine systems converging to an invariant set is developed in the framework of the sampling-based switching, for which the lengths between successive sampling instants are assumed to be fixed. The corresponding sampled-based switching rules are obtained by solving a family of the linear matrix inequalities. Subsequently, these sampling lengths are extended from a fixed value to a certain interval and robust switching rules are obtained. Systems using these switching rules have the insensitivity to sampling period perturbation. Finally, an application to a DC–DC converter is provided to demonstrate the effectiveness of the proposed method.