摘要： In[1] the optimal stochastic control problem of linear discrete-time system is discussed when the state noise has no delay.In[2] the optimal stochastic control problem is discussed when the state noise has a delay and the noise is independent of the measurement noise.The paper composes of two parts.In §1 the stochastic control problem is discussed when the system contains non-stochastic input (the system with the state noise for which mean value is not zero can be transformed into this case) and the state noise is mutually dependent on the measurement noise In §2 the filter and the optimal stochastic control problem is discussed with the Moor-Penrose inverse when the state noise and the measurement noise are one-step correlated.In this paper the optimal control law is given which coincides with the separation principle.