Stabilizing switching rule design for affine switched systems

We propose a method for designing switching rules that can drive the state of the switched dynamic system to a desired equilibrium point. The method deals with the class of switched systems where each sub-system has an affine vector field. The results are given in terms of linear matrix inequalities and they guarantee global asymptotic stability of the tracking error dynamics even if sliding motion occurs along a switching surface of the system. The switching rules are based on complete and partial state measurements. Two examples are used to illustrate the approach.