Theoretical interpretation for some relationships in H∞ setting

The paper discusses relationships between the H_∞ preview control and the standard H_∞ control, between the H_∞ fixed-lag smoothing and the H_∞ filtering. It is easy to understand intuitively that the H_∞ preview control problem is inevitably solvable if the standard H_∞ control problem for the identical system is solvable and that the H_∞ fixed-lag smoothing problem is solvable as the H_∞ filtering problem is solvable for the same system and measurements. However, the theoretical interpretations for these two phenomenons so far have not been found in any existing literatures. Hence, the paper makes use of Innovation Re-organization analysis to derive and provide a rigorous and theoretical interpretation for the relationships, which are very similar to the relationship between the H₂ smoothing and the H₂ filtering.