Finite-time guaranteed state estimation for discrete-time systems with disturbances

In this paper, we consider a family of discrete-time systems with input and output. A new technique, which is reminiscent of a construction of finite-time observers for continuous-time systems, is proposed for discrete-time case. The systems are affected by additive disturbances and noises. Exact estimation or approximate estimation can be achieved depending on the absence or the presence of unknown but bounded uncertainties, respectively.