An Adaptive Sliding Mode Observer Design for Systems Subject to Mismatched Uncertainties

This paper is concerned with the state estimation of systems subject to matched/mismatched system uncertainties and disturbances. An adaptive strategy is applied to the sliding mode observer so that the approaching condition can be achieved in a more effective and efficient manner. Nevertheless, due to the existence of mismatched uncertainties, the sliding motion is no longer invariant, and the state observation performance may deteriorate with an inappropriate selection of the observer gain. Furthermore, in the case that the invariant zeros do not lie in the left half-plane, the use of state transformations is need to stabilize the sliding mode observer, and then the (mis)matched perturbation terms will also affect the responses of the reduced-order dynamics. To guarantee stability of the observer error dynamics and achieve better estimation performance simultaneously, a trade-off between both aims is considered to determine the observer gain. The existence of the solution is characterized via linear matrix inequalities. Numerical studies are presented to demonstrate the feasibility and effectiveness of the proposed approach.