Implicit volterra series interpolation for model reduction of bilinear systems

Research paper by Mian Ilyas Ahmad, Ulrike Baur, Peter Benner

Indexed on: 22 Oct '16Published on: 20 Oct '16Published in: Journal of Computational and Applied Mathematics


We propose a new interpolatory framework for model reduction of large-scale bilinear systems. The input-output representation of a bilinear system in frequency domain involves a series of multivariate transfer functions, each representing a subsystem of the bilinear system. If a weighted sum of these multivariate transfer functions associated with a reduced bilinear system interpolates a weighted sum of the original multivariate transfer functions, we say that the reduced system satisfies a Volterra series interpolation Flagg and Gugercin (2015). These interpolatory conditions can also ensure the necessary conditions for H2H2-optimal model reduction Flagg and Gugercin (2015), Benner and Breiten (2012). We observe that, by carefully selecting the weights of the series, the Volterra series interpolatory conditions are transformed to the problem of interpolating a linear system with an affine parameter dependence. Such linear parametric systems can then be reduced by some method for parametric model order reduction.

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