Simultaneous Unknown Input And Sensor Noise Reconstruction For Nonlinear Systems With Boundary Layer Sliding Mode Observers

While sliding mode observers (SMOs) using discontinuous relays are widely analyzed, most SMOs are implemented using a continuous approximation of the discontinuous relays. This continuous approximation results in the formation of a boundary layer in a neighborhood of the sliding manifold in the observer error space. Therefore, it becomes necessary to develop methods for attenuating the effect of the boundary layer and guaranteeing performance bounds on the resulting state estimation error. In this paper, a method is proposed for designing boundary-layer based SMOs for simultaneously reconstructing system states and unknown inputs in the presence of measurement noise. The proposed scheme is attractive because (i) it generalizes existing SMO schemes to a wider class of nonlinear systems; (ii) observer gains are computed using linear matrix inequalities; and, (iii) the unknown input and measurement noise are reconstructed simultaneously. Two numerical examples are presented to illustrate the performance of the proposed scheme and verify that the pre-computed bounds on the error state are satisfied.