$H_{\infty}$ Unbiased Filtering for Linear Descriptor Systems via LMI

This note concerns the optimal $H_{\infty}$ unbiased filtering problem for linear descriptor systems. It unifies the design of reduced-order, minimal-order and full-order filters for continuous and discrete-time systems. Necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of linear matrix inequalities (LMIs). The parametrization of all $H_{\infty}$ unbiased filters is presented. Application to standard systems with or without unknown inputs is given. A numerical example is given to show the applicability of the presented approach.