Disturbance observer-based adaptive fixed-time sliding mode control for nonlinear time-delay systems

This paper develops a disturbance observer-based adaptive sliding mode control strategy for a class of nonlinear time-delay systems subject to exogenous disturbances and delayed nonlinear uncertainties. A fixed-time nonlinear disturbance observer is designed using dual-power feedback terms to achieve precise estimation of external disturbances. Barrier functions are employed to design an adaptive controller that dynamically adjusts gains for time-delay uncertainty compensation, removing the initial condition dependence of common approaches. The Lyapunov-Razumikhin method is employed to handle large time-varying delays, and the fixed-time convergence of the sliding surface is established through Lyapunov stability theory. The effectiveness of the proposed method is validated through its application to a continuous stirred-tank reactor system and a numerical simulation.