Nonlinear sliding mode observers for state and unknown input estimations

Sliding mode observers (SMO) for nonlinear uncertain systems are discussed from the perspective of the observability of unknown inputs. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. A new nonlinear transformation is proposed and it divides the original system into two interconnected subsystems. The existence of sliding mode observers completely relies on the observability of unknown inputs w.r.t. output measurements. The robust terms or switching terms are designed such that the unknown inputs are tracked by their robust terms and so can be reconstructed from the sliding mode. The conditions for asymptotic stability of estimation error dynamics have been derived, based on Lipschitz assumptions for nonlinear functions, via standard Lyapunov analysis.