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Abstract
Two-sided projection methods are presented for model reduction of large scale multi-input multi-output bilinear systems. By properly choosing projection matrices, the reduced model possesses a superior moment matching property and we prove it from a new perspective by means of linear equations. The preservation of stability for reduced models is also considered. In contrast to the most existing approaches, we construct the reduced model directly instead of using an iterative procedure, thereby saving much computational cost. As two-sided methods are more likely to produce badly ill-conditioned system matrices, a mixed algorithm having the benefits of one-sided and two-sided methods is proposed at the cost of roughly doubling the dimension of reduced models. Theoretical analysis and numerical experiments show the efficiency of our approach.
Acknowledgements
The authors would like to thank the editors and the anonymous referees for their helpful comments and suggestions which greatly improved the presentation of the paper.
This work was supported by the Natural Science Foundation of China (NSFC) under grant 11071192, the International Science and Technology Cooperation Program of China under grant 2010DFA14700, and the NPU Foundation for Fundamental Research under grant JCY20130142.