Recursive input reconstruction with a delay

The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several wide-spread applications. In this paper we consider recursive reconstruction of unknown inputs with a delay for both square and non-square systems. That is, we develop filters that use current measurements to estimate past states and reconstruct past inputs. We further develop convergence results for these filters and show that the convergence of these filters are related to multivariable zeros of the systems. Finally we also show that existing unbiased minimum-variance filters are special cases of the proposed filters.