A discrete time linear stochastic system with random horizon of control is considered. Disturbances in the system have distribution belonging to an exponential family with a parameter. The loss function depends on state variables, controls and it is given by (3). A horizon of control is a random variable independent of disturbances with given distribution. For a conjugate a priori distribution of the parameter the BAYES control is obtained. Next, a problem of determining the minimax control of the system is considered.