On the optimal stabilization of not completely controlled systems

The problem of the optimal stabilization of a controlled system is considered in the paper when the minimizing functional is sign-constant and the system becomes stable only in the sense of the acting force [4]. In the general case, sufficient conditions are attained, according to which it is possible to solve the problem of the optimal stabilization by the acting force. For the linear differential equations with constant coefficients Lyapunov function is constructed and the optimal control actions are defined, which make the system stable in the sense of the acting force.