Abstract: The optimal control problem for the discrete time stochastic singular systems with linear quadratic cost functional is discussed.The problem is first transformed into an equivalent normal form via an output feedback and a state transformation and then solved by utilizing standard result for the normal systems. Because of using the output feedback,an optimal con-trol law derived consists of linear feedbacks of measure outputs and part states. This form of the control law can be realized in engineering.the filtering and Riccati equations obtained in his way are only of order n1,which reduces p orders in comparison with Ref.[ 5].Thus com putational quantity can be decreased greatly. On the other hand,the direct effect on the control law by dynamic noises is avoided because the control law includes no estimation of dynamic noises.

Key words: distrubution functions, quadratic equations, optimal control, statistical distrubu-eons