Feedback control for damping a system of linear oscillators

The paper is devoted to a design of a common bounded feedback control steering a system of an arbitrary number of linear oscillators to the equilibrium. At high energies, the control is based on the asymptotic theory of reachable sets of linear systems. With decreasing of the energy, a similar control with a reduced upper bound is used. On the final stage, the control is constructed by using the method of common Lyapunov functions. Special attention is paid to the cases of one and two oscillators.