From the text: This paper considers the problem of synthesizing a bounded control of a linear dynamical system satisfying the Kalman controllability condition. An approach is developed which makes it possible to construct feedback control laws transferring the system to the origin in finite time. The approach is based on methods of stability theory. The construction is based on the notion of a common Lyapunov function. It is shown that the constructed control remains effective in the presence of uncontrollable perturbations of the system. As an illustration, results of numerically modeling the dynamics of a second-order system controlled by the law proposed in the paper are presented.