Optimal unbiased filtering via linear matrix inequalities

Solutions to the optimal H/sub /spl infin// and L/sub 2/-L/sub /spl infin// unbiased reduced-order filtering problems are obtained in terms of linear matrix inequalities (LMIs). The order of the optimal filter is equal to the number of measurements. Both continuous-time and discrete-time results are presented. An explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix.