Stabilization of a class of singularly perturbed switched systems

In this paper, we address the control of a class of switched systems cast in the framework of singularly perturbed systems. The class of switched systems that we deal with here is a particular case of switched affine systems where the state matrices are the same for all modes. These systems have been studied in the literature, wherein control design is carried out by solving Linear Matrix Inequalities (LMIs). However, the presence of the small parameter ε, characteristic of singularly perturbed systems, in the dynamical equation introduces numerical stiffness. To the best of the authors’ knowledge, these issues have not been addressed in the literature for the class of switched systems studied here. We propose an ε-dependent controller stabilizing the system and also an ε-independent controller, in the case where the parameter ε is not well-known. The design of these control laws is based on LMIs that do not present the ill-conditioning linked to ε. The proposed approach is illustrated by simulation results.