Robust H₂ filtering of linear systems with time delays

The problem of robust H₂ estimation of a combination of states of a stationary linear system with time delays is considered. Since the problem is infinite is dimensional in nature, an attempt is being made to develop finite dimensional methods that will guarantee a preassigned estimation accuracy. The approach of minimizing the trace of a matrix that overbonds the exact covariance of the estimation error is considered. Sufficient conditions are given in the form of linear inequalities (LMIs). The results are illustrated by a numerical example.