This study deals with the problem of robust H ∞ finite-time boundedness analysis and design of finite-time H ∞ feedback control for discrete switched systems. By using sojourn probability information, a new kind of switched system model is proposed. Based on this model, sufficient conditions for the H ∞ finite-time boundedness are obtained by using Lyapunov functional method and the corresponding controllers are also designed. Moreover, when considering partially known probabilities and unknown system uncertainties, the analysis and design methods are also given. Finally, an example is given to illustrate the efficiency of the proposed method.