A discrete time variable structure observer for uncertain systems with measurement noise

Abstract

This paper further develops the discrete-time sliding mode observer (DSMO) of Thein and Misawa (2001) and Thein (2002). The state estimation technique allows for measurement noise and bounded matched and unmatched uncertainties/disturbances. This DSMO has an overlapping set of boundary layers. In double boundary layer DSMO (DBL-DSMO), the DSMO has an attractive outer boundary layer to which state estimate errors converge. In spite of measurement noise, it is guaranteed that the state estimates do not chatter along the outer boundary layer and, in fact, converge to within the outer boundary layer to the smallest existing inner boundary layer which satisfy given stability requirements. Within this inner boundary layer, state estimate errors are proven to have a finite bound. This inherent effect facilitates a convenient and efficient way of choosing observer parameters. The DSMO is implemented on a second order resonance model with unmatched uncertainties and with measurement noise. In this paper, the behavior and effects of the outer boundary layer, and resulting inner boundary layer, are seen.