Discrete-time Observers with Multiple Sliding Modes for a Class of Nonlinear Uncertain Systems

This paper designs discrete-time sliding mode (DSM) observer design for a class of nonlinear uncertain systems. The Taylor series expansion and nonlinear transformation are used to convert the nonlinear continuous time system into the discrete-time model. Multiple sliding modes were introduced to compensate for multiple disturbance terms in the subsystems by appending them to a constant gain observer. A strategy is developed to guarantee the convergence of the estimation error to a bound within a specified boundary layer. Existence of discrete-time sliding mode is guaranteed and the relation between the boundary layer thickness and the sliding mode gain design are obtained