Sliding mode control with adaptive VSS observer

The conventional sliding mode control and variable structure control (VSC) of nonlinear uncertain system are well known for their robust property and simplity of control law. However, the use of them is only pardonable on the assumption that the upper-bound of parameter variation or nonlinearity is known and that the complete information about state is available. Though the former has been solved with adaptive robust control theory recently, the latter seems not to be solved. In this paper, we try to solve this problem using the technique of VSS adaptive robust control theory. That is, we propose a VSS adaptive observer and a sliding mode control incorporated with this observer. We can prove the robust stability of the closed system applying the Lyapunov's second method.