An Innovation Approach to $H_{\infty }$ Fixed-Lag Smoothing for Descriptor Systems
The finite horizon Hinfin fixed-lag smoothing problem for linear descriptor systems is considered and a sufficient condition for the existence of an Hinfin smoother is derived. The key approach applied for deriving the Hinfin fixed-lag smoother is the re-organization innovation analysis in Krein space. Under the Krein space, the Hinfin 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 Hinfin smoothing is given. At last, an illustrative example shows the efficiency of the proposed estimator