Exogenous Input Reconstruction for Nonlinear 1 Systems Using Sliding Mode Observers and Smooth

Abstract. While sliding mode observers (SMOs) using discontinuous relays are widely analyzed, 9 most SMOs are implemented computationally using a continuous approximation of the discontin10 uous relays. This results in the formation of a boundary layer in a neighborhood of the sliding 11 manifold in the observer error space. In this paper, a convex programming method for constructing 12 boundary-layer SMOs (BL-SMOs) is presented for a wide class of nonlinear systems characterized 13 by incremental quadratic constraints. Specifically, the observer gains are computed by solving a 14 set of linear matrix inequalities and ultimate bounds on the state of a synthetic descriptor system. 15 A novel application of filtering using smooth window functions (SWFs) is leveraged to reconstruct 16 the unknown exogenous inputs to prescribed accuracy. Two numerical examples are presented to 17 illustrate the effectiveness of the proposed approach. 18