This paper considers the problem of stability and robust H∞ stabilization for a class of uncertain switched systems using the delta operator. Based on multiple Lyapunov function method, a sufficient condition for the existence of stability of the delta operator switched system is presented, and the design approach to robust H∞ state feedback controller is addressed. The proposed controller can robustly stabilize the uncertain delta operator switched system, and also guarantee H∞ performance of the closed-loop system for all admissible parameter perturbations. The solution to the controller is formulated in the form of a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of the developed method.