H∞ smoothing in discrete-time: a direct approach

The H_∞ fixed-lag smoothing problem for discrete-time linear systems is considered. It is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system. However, in order to check the solvability of the smoothing problem and compute the relevant gains one must solve a Riccati equation involving the augmented system matrices, an approach that may be inefficient, especially for long lags. In this paper, efficient algorithms are worked out that permit to check solvability and implement the smoother relying only on the solution of the H_∞ filtering Riccati equation. In particular, this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.