A Model-Based Extended State Observer for Discrete-Time Linear Multivariable Systems

A model-based extended state observer (MB-ESO) and its variant are proposed for discrete-time linear multivariable systems, where multiple disturbances are defined as an extended state vector in the same manner as in the original formulation of ESO. The variant MB-ESO extends the MB-ESO to address cases where the disturbance gain matrix is non-diagonal. Leveraging the connection between the variant MB-ESO and the well-known unknown input observer (UIO), the condition for the existence of a MB-ESO and its variant in multivariable systems is established, for the first time, i.e., no invariant zeros exist between the disturbances and the plant outputs. It is shown that, with the observer eigenvalues all placed at the origin and the subsystems decoupled, the variant MB-ESO produces the identical disturbance estimation as that of UIO. Moreover, the error characteristics of MB-ESO and its variant are analyzed and the transfer functions associated with the disturbance estimation errors are derived. It is demonstrated both mathematically and in simulations that the disturbance estimation error of MB-ESO decreases monotonically with respect to both the observer eigenvalues and time.