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Stability-Preserving Rational Approximation Subject to Interpolation Constraints

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2 Author(s)
Johan Karlsson ; Dept. of Math., R. Inst. of Technol., Stockholm ; Anders Lindquist

A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational analytic interpolants with an a priori bound, has been developed in recent years. In this paper, we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H 2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded analytic interpolants.

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IEEE Transactions on Automatic Control  (Volume:53 ,  Issue: 7 )