H∞ fixed-lag smoothing for descriptor systems

In this paper, we study the finite horizon H_∞ fixed-lag smoothing problem for linear descriptor systems. The key approach applied for deriving the H_∞ fixed-lag smoother is the re-organization innovation analysis in Krein space. Under the Krein space, the H_∞ fixed-lag smoothing is converted into an H₂ estimation problem for the system with current and delayed measurements. By using innovation re-organization approach, the H₂ estimation with delayed measurements is transformed into a problem of delay-free measurements and thus a simple solution to H_∞ smoothing is given.