Abstract: The multiple Lyapunov function is used to study the robust H∞ control of a class of linear discrete switched systems with time-varying/delaying uncertainties. Assuming that the H∞ control cannot be implemented in each individual subsystem and based on switching state feedback control, a delay-dependent and LMI (linear matrix inequalities)-based sufficient condition is given for the system implementation of robust H∞ control. In addition, the designs of switching law and robust H∞ controller are given, with the relationship between time-delay bound and H∞ performance discussed. A simulation example is given to show the validity of the results.