Robust generalized H2 filtering — The finite-horizon case

In this paper the robust finite-horizon H₂ estimation problem of a linear time-varying system is addressed in a very general way in order to face the finite-horizon filtering problem and, consequently, the fixed-lag forward-backward non-causal estimation problem. The quantity to be estimated is a generic linear combination of the state, of the input and of a suitable signal representing the uncertainty. In such a way the deconvolution problem and some type of fault detection problems are treated as particular cases. Furthermore, the so-called singular case is treated as well.