Stabilization of nonlinear Lipschitz systems with input delay and disturbances using state and disturbance predictors

This paper proposes an algorithm for stabilizing nonlinear Lipschitz systems with a known constant input delay and an unknown bounded disturbance. The control law is designed based on both a state predictor and a disturbance predictor. The stability of the closed-loop system is established using the Lyapunov-Krasovskii functional method, which provides sufficient conditions in the form of a feasible linear matrix inequality (LMI). The ultimate boundedness of all system signals is formally proven. Furthermore, it is shown that the derived LMI is influenced by system parameters, sector bounds of the nonlinearity, and the delay, allowing for the determination of their limit values while ensuring system stability. The effectiveness of the proposed approach is validated through numerical simulations in MATLAB/Simulink.