Nonlinear Discrete-time Sliding Mode Observations with Application to a Three-phase Current Motor

This paper addresses the problems of discrete-time state and unknown input estimation for continuous-time nonlinear systems with multiple unknown inputs. The conditions for the observability of unknown inputs w.r.t. outputs are discussed. The novelty lies in the formulation of multiple sliding modes estimator for the states that are directly influenced by unknown inputs, which cannot be decoupled by nonlinear transformation. This framework allows for the estimation of unknown inputs from the multiple sliding modes. Existence of discrete-time sliding mode is guaranteed and the relation between the boundary layer thickness and the sliding mode gain design that will eliminate chattering and the boundedness conditions are obtained.