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

In the absence of a detailed and accurate plant model, extended state observer (ESO) has been clearly shown as an effective tool in both control applications and theoretical analysis. Less clear is how to further enhance such a tool when the model is available, however inaccurate, together with additional measurement information. To this end, a model-based ESO (MB-ESO) and its generalized form (GMB-ESO) for discrete-time linear multivariable systems are developed in this paper by explicitly incorporating the additional state-space model and measurement information, which is otherwise bypassed by the conventional ESO. In addition, GMB-ESO is shown to accommodate systems with non-diagonal disturbance gain matrices. Necessary and sufficient conditions for the existence of the MB-ESO and GMB-ESO are established in terms of a well-defined disturbance vector relative degree and the absence of invariant zeros in the disturbance-to-measurement path. Under noise-free measurements and infinite observer bandwidth, exact disturbance reconstruction can be achieved within a finite number of steps, while under measurement noise, \(\varepsilon\)-accurate reconstruction can be guaranteed with finite observer bandwidth. Finally, the disturbance recontruction error of the MB-ESO is shown, in both theoretical analysis and simulation, to decrease monotonically with time, when the disturbance gain matrix is diagonal, and an explicit bound on the disturbance estimation error is derived.