Optimal unbiased reduced order filtering for discrete-time descriptor systems via LMI

In this paper, the reduced order unbiased optimal H∞H∞ filtering problem for discrete-time descriptor linear systems is considered. Necessary and sufficient conditions for the existence of unbiased causal time invariant filters are obtained. Solutions of the filtering problems are given in terms of linear matrix inequalities (LMIs). Parametrization of all optimal causal unbiased filters is provided. The proposed method generalizes the existing results in the standard case.