Switching rule design for affine switched systems with ℋ∞ performance

In this paper we consider the class of affine switched systems subject to ℒ
₂
disturbances and we propose a method for switching rule design such that an upper bound on the disturbance gain, in the ℋ
_∞
sense, is minimized. In the absence of disturbances the switching rule drives the state of the switched system to a desired equilibrium point. 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 on any switching surface of the system. An example is used to illustrate the approach.