Feedback linearization of nonlinear time-delay systems over a time window via discontinuous control

Feedback linearization is worked out for nonlinear time-delay systems and it is shown that even if the problem can not be solved for all time, it may still be solved over some time windows. The solution then reduces to a discontinuous state feedback. It is foreseen that such piecewise feedback linearization can be instrumental for stabilization by a discontinuous control, although it is not the scope of this paper. The approach used herein may be used to address other classical control problems. It takes advantage of the delays as delays duplicate somehow the number of independent control values at some given time instant.