An Innovation Approach to H∞ Fixed-Lag Smoothing for Descriptor Systems

The finite horizon H_infin fixed-lag smoothing problem for linear descriptor systems is considered and a sufficient condition for the existence of an H_infin smoother is derived. The key approach applied for deriving the H_infin fixed-lag smoother is the re-organization innovation analysis in Krein space. Under the Krein space, the H_infin fixed-lag smoothing is converted into an H₂ estimation problem for the system with current and delayed measurements. By using innovation re-organization approach, we show that the H₂ estimation with delayed measurements is transformed into a problem of delay-free measurements and thus a simple solution to H_infin smoothing is given. At last, an illustrative example shows the efficiency of the proposed estimator