On stabilization of the controlled mechanical systems

Consideration was given to stabilization of the equilibrium of the controlled stationary mechanical systems with controllers which take into account only the delay in coordinate. The theorem of asymptotic stability of the retarded nonautonomous functional differential equation with infinite delay was proved. The study was based on the method of limiting equations and the Lyapunov functionals with fixed-sign derivative. The problem of stabilization of triaxial orientation of a solid body in the inertial coordinate system was considered as an example.