  The present paper is mainly aimed at introducing a novel notion of stability
of nonlinear time-delay systems called Rational Stability. According to the
Lyapunov-type, various sufficient conditions for rational stability are
reached. Under delay dependent conditions, we suggest a nonlinear time-delay
observer to estimate the system states, a state feedback controller and the
observer-based controller rational stability is provided. Moreover, global
rational stability using output feedback is given. Finally, the study presents
simulation findings to show the feasibility of the suggested strategy.
