State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques

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