Abstract
In this paper, a dimension reduction method via general orthogonal polynomials and multiorder Arnoldi algorithm is proposed, which focuses on the topic of structure-preserving for k-power bilinear systems. The main procedure is using a series of expansion coefficient vectors of each state variables in the space spanned by general orthogonal polynomials that satisfy a recurrence formula to generate a projection based on multiorder Arnoldi algorithm. The resulting reduced-order model not only matches a desired number of expansion coefficients of the original output but also retains the topology structure. Meanwhile, the stability is well preserved under some certain conditions and the error bound is also given. Finally, two numerical simulations are provided to illustrate the effectiveness of our proposed algorithm in the views of accuracy and computational cost.
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Zhen-Zhong Qi
Zhen-Zhong Qi received the PhD degree from Xi'an Jiaotong University (XJTU), China. He is currently a lecturer in department of mathematics, Northwest University, China. He focuses on applying mathematics and computation to solve science and engineering problems. His research interests include model order reduction, control theory and circuit simulation.
Yao-Lin Jiang
Yao-Lin Jiang is a full professor (Changjiang Scholar in China, too) at the School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China. He has published 4 books and about 230 papers in journals. His research interests include theoretical studies of engineering problems, model order reduction, waveform relaxation, numerical solutions of differential equations, dynamics of non-linear systems, circuit simulation and parallel processing.
Zhi-Hua Xiao
Zhi-Hua Xiao received his PhD degree from Xi'an Jiaotong University, Shaanxi, China, in 2015. He is an associate professor in the School of Information and Mathematics at Yangtze University. He has published about 20 papers in journals. His research interests include theoretical studies of control systems, model order reduction and numerical linear algebra.