Structure-preserving interpolation of bilinear control systems
Peter Benner, Serkan Gugercin, Steffen W. R. Werner
Abstract
Abstract In this paper, we extendthe structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.
Topics & Concepts
Bilinear interpolationMathematicsInterpolation (computer graphics)Reduction (mathematics)Applied mathematicsLinear interpolationNearest-neighbor interpolationBilinear mapTransfer functionStairstep interpolationLinear systemSymmetric bilinear formMatrix (chemical analysis)Trilinear interpolationBilinear transformBirkhoff interpolationBicubic interpolationPolynomial interpolationComputational Science and EngineeringAlgebra over a fieldControl systemCalculus (dental)Inverse quadratic interpolationType (biology)Bilinear formAlgorithmMultivariate interpolationMathematical optimizationFunction (biology)Spline interpolationTransfer (computing)Model Reduction and Neural NetworksMatrix Theory and AlgorithmsTensor decomposition and applications