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

Abstract

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.

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

“…The dynamics of states that are measured as outputs (11) of 'm' subsystems have the structure as in (9).…”

“…For details of inverse nonlinear transformation, the selection of sampling period T s , and the design of feedback gain readers may refer to [3], [9].…”