Abstract: The problem of dual control is studied for the stochastic system of which the uncertainty model is polytopic.First,it is assumed that the polytope exists in the system matrix,input matrix and measure matrix of the state space model.Second,with the posterior probability weighting of the uncertain parameters,an augmented system is obtained for the uncertainty model.Then,the suboptimal control law is achieved using the dynamic programming principle.Finally,the feasibility and effectiveness of the presented approach are verified with simulation.