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On the stabilization of input delayed oscillators

The problem of globally asymptotically stabilizing by bounded feedback an oscillator with an arbitrary delay in the input is solved. A first solution is deduced from a general result on the global stabilization of null controllable linear systems with delay in the input through bounded control laws with a distributed term. Then it is shown through a Lyapunov analysis that the stabilization can be achieved as well when the distributed terms are neglected. It turns out that this result is intimately related to the issue of the output feedback stabilization of oscillators.