Global rational stabilization of a class of nonlinear time-delay systems

TL;DR

This paper introduces the concept of Rational Stability for nonlinear time-delay systems, providing new stability criteria, observer design, and control strategies with simulation validation.

Contribution

It proposes a novel notion of Rational Stability, along with delay-dependent conditions, observer-based controllers, and output feedback methods for nonlinear time-delay systems.

Findings

Established sufficient conditions for Rational Stability.

Designed a nonlinear time-delay observer and controllers.

Validated strategies through simulation results.

Abstract

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.