Reduced order filtering in an H∞ setting

In this paper we consider the problem of estimation with reduced order filter/observers with an H∞ type performance criterion. For a give n-th order linear system, we give necessary and sufficient conditions for there to exist an "Unbiased" (precise definition given in the Definition 2 of the paper) filter of order l ≪ n to estimate l states of the system. When the necessary and sufficient conditions ar met, state space formulae are given for a reduced order filter that achieves the desired performance.