Hankel-norm approximation of large-scale descriptor systems

Hankel-norm approximation is a model reduction method for linear time-invariant systems, which provides the best approximation in the Hankel semi-norm. In this paper, the computation of the optimal Hankel-norm approximation is generalized to the case of linear time-invariant continuous-time descriptor systems. A new algebraic characterization of all-pass descriptor systems is developed and used to construct an efficient algorithm by refining the generalized balanced truncation square root method. For a wide practical usage, adaptations of the introduced algorithm towards stable computations and sparse systems are suggested, as well as an approach for a projection-free algorithm. To show the approximation behavior of the introduced method, numerical examples are presented.

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