The observation problem along with the certain independent value plays a great role while carrying out control of dynamic systems in the conditions of uncertainty (Kalman, 1957, Krasovski, 1985, Leondes, 1976). A new approach on connection between the problems of control and observation is presented in (Gabasov, 1991). Developing it, we justify the solution of observation problem in the given paper that arises, at optimization of linear dynamic systems. The paper consists of the two parts. In the part I the linear discrete system is investigated. In the part II the linear dynamic continuous system is considered.