Plenary session Current trends in the development of mathematical control theory at the faculty of applied mathematics and control processes SPbSU At the beginning of the report, a historical overview of the fundamental problems of control theory is presented, the need to solve which served as a motivating for the base of a new faculty at Leningrad State University. Further developments led to the creation of twenty departments specializing in the development of mathematical models and control methods in various sectors of the industry. The scientific school created by Vladimir Ivanovich Zubov is known all over the World. One of the directions of scientific school is connected with the development of theory and applications to models described by dynamic systems with delay. On this way the basic results in the theory of robust stability of the differential-difference systems were obtained. In the late 90-ies of the last century, these results played a significant role in the design of the tokomak ITER. The transfer problem of the A. M. Lyapunov's criterion on the analysis of the ordinary differential system stability by a direct method at first on linear systems of differential-difference equations, and then on nonlinear homogeneous systems was solved. At the end of the report some new problems available for students, postgraduates and young employees will be formulated.