The problem of robust H∞ control of uncertain linear switched system with dwell time is addressed. A Lyapunov function in a quadratic form, which is non-increasing at the switching instances, is assigned to each subsystem. This function is used to determine the stability and the L 2 -gain of the switched system, where a bounded real lemma (BRL) is derived that provides an upper-bound to the system L2 -gain over the uncertainty polytope. The obtained results are used to solve the corresponding problem of robust H∞ state-feedback control for cases where the switching signal is either measured online, or is unknown. A numerical example is given which demonstrates the applicability of the theory developed to the control of switched systems.