A discrete time variable structure observer with overlapping boundary layers

This paper further develops the Discrete-Time Sliding Mode Observer (DSMO) of Thein and Misawa (2001). The state estimation technique allows for bounded matched and unmatched uncertainties/disturbances and has an overlapping set of boundary layers. In this presentation of the Double Boundary Layer DSMO (DBL-DSMO), the DSMO has an attractive outer boundary layer to which state estimate errors converge. In addition, 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 satisfies given stability requirements. Within this inner boundary layer, state estimate errors axe 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 process noise. Here, the behavior and effects of the outer boundary layer, and resulting inner boundary layer, are seen.