Delayed unknown input observers for discrete-time linear systems with guaranteed performance

In this paper, we propose a state and unknown input observer for discrete-time linear systems with bounded unknown inputs and measurement disturbances. The design procedure is formulated using a set of linear matrix inequalities, and leverages delayed (or fixed-lag) estimates. The observer error states and/or user-defined performance outputs are guaranteed to operate at certain performance bounds. Furthermore, by employing sufficiently large delays, the observer is guaranteed to provide exact asymptotic state and input estimates for minimum-phase systems. We demonstrate, via numerical examples, that the proposed observer can be used for a wider class of systems than those satisfying matching conditions.