Sliding mode observer for a class of globally Lipschitz non-linear systems with time-varying delay and noise in its output

In this study, the state estimation problem for a class of globally Lipschitz non-linear systems with time-varying delayed output is addressed based on sliding mode observer. One of the contributions is the stability properties of the proposed observer are studied in the presence of state perturbation and measurement noise. By using the Lyapunov-Razumikhin approach, the asymptotic convergence properties for the estimation error is ensured. The assumption on the state perturbation and measurement noise is that they need to be bounded. Moreover, the proposed observer is applied into the model of aircraft longitudinal motion and simulation results illustrate the performance of the proposed observer.