Robust sliding mode observer with parameters estimation for a class of nonlinear time-delay systems

In this paper, a class of time delayed nonlinear systems is considered where both parametric uncertainty and structural uncertainty are involved. The delay is time-varying and the unknown parameters are embedded in the system nonlinearly. The only limitation on the structural uncertainty is that its bound is known. A sliding mode observer is proposed to estimate the system state and an adaptive law is proposed to estimate the unknown parameters simultaneously. By using the Lyapunov-Razuminkhin approach, sufficient conditions are developed such that the error system is uniformly ultimately bounded. A simulation study on a bioreactor system shows the effectiveness of the approach.