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Global asymptotic stabilization of a chain of integrators with a time-varying delay in the input by output feedback

In this paper, we consider a stabilization problem of a chain of integrators which allows a time-varying delay in the input. Among the plethora of papers on the stabilization of input-delayed chain of integrators, the existing results are only with constant delays. We show that with the proposed output feedback controller, the considered system can be globally asymptotically stabilized as long as the time-varying delay is bounded by a finite constant. That is, the time-varying rate is irrelevant in the stability result.