Robust discrete-time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete-time nonlinear sliding mode observer for state and unknown input estimations of a class of single-input/single-output nonlinear uncertain systems. The uncertainties are characterized by a state-dependent vector and a scalar disturbance/unknown input. The discrete-time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete-time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright # 2006 John Wiley & Sons, Ltd.