Distributed unknown input observers for discrete-time LTI systems

In this paper we consider the problem of distributed estimation of the state of a discrete-time, linear and time-invariant (LTI) state space model affected by disturbances. We assume that there is a connected network of sensors having access to some output measurements as well as to part of the control inputs applied to the system. Such sensors exchange information with the goal of achieving consensus and providing an asymptotically correct estimate of the original system state. Necessary and sufficient conditions for the existence of distributed unknown input observers with augmented states that achieve both goals are derived. The problem solution exploits the theory of decentralized output feedback control, thus making it possible to inherit the algorithms available for the solution of that problem.