A generalized Schur algorithm in the Krein space and its application to H∞-filtering

This paper introduces a generalized Schur algorithm in the Krein space with an indefinite inner product. Concepts such as Caratheodory classes and Schur classes used in the classical Schur algorithm cannot be applied in the Krein space since the positive-definiteness corresponds merely to the nonsingularity in the Krein space. We note also that these problems appear when fast algorithms for suboptimal H ^∞ filtering are implemented. We derive the extended Chandrasekhar algorithm which is a fast implementation of H^∞ filtering, and explain the connection between the generalized Schur algorithm and the Chandrasekhar algorithm. Using this result it is possible to derive a fast algorithm for suboptimal H^∞ filtering