Switching Rule Design for Switched Dynamic Systems With Affine Vector Fields

In this paper, we propose a method for designing switching rules that drive the state of the switched dynamic system to a desired equilibrium point. The method deals with the class of switched systems where each mode of operation is represented by a dynamical system with 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. Switching rules based on complete and partial state measurements are proposed. The case of uncertain polytopic systems is also considered and a numerical example illustrates the approach.