LMI-based Control of Singularly Perturbed Switched Affine Systems

In this paper, we tackle the problem of stabilizing singularly perturbed switched affine systems. Even though efficient control strategies based on the solution of Linear Matrix Inequalities (LMIs) have been presented in the switched affine systems literature, the presence of the small singular perturbation parameter may introduce numerical difficulties in the solution of these LMIs due to ill conditioning. Moreover, this parameter may be uncertain or its use in the control law may not be practical. Here, we propose an LMI-based control design strategy that avoids the conditioning issues and that also provides an estimation of the domain of attraction. Furthermore, the resulting controller does not depend on the singular perturbation parameter. The proposed method is illustrated on a numerical example.