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Model reduction for robust control: A Schur relative error method. (English) Zbl 0731.93013
According to the robustness theorem included in the section 2 of this paper, an approximate model is useful for control design if it has relative error less than one through the control bandwidth, thus underscoring the importance of relative error methods for model reduction.
The section 3 summarize results on balanced stochastic reduction. In section 4 a general procedure for calculating a realization of the kth order obtained by using arbitrary bases for the left and right eigenspaces associated with the biggest eigenvalues of PQ (P (resp. Q) is a reachability (resp. an observability)) Grammian. The numerical robustness of this procedure depends on how the preceding bases are computed; the authors propose a procedure based on Schur decomposition of PQ, and a square root method. Two examples are presented to demonstrate the interest of the proposed algorithms.

MSC:
93B11 System structure simplification
93B35 Sensitivity (robustness)
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