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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. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model order reduction (MOR) method based on general orthogonal polynomials for K-power bilinear systems in the time domain. Constructing proper projection matrices by solving a series of linear equations, a reduced K-power bilinear system is produced, which preserves the original coupled structure. It can match several expansion coefficients of the original output. Then the error bound of our algorithm is also investigated. Moreover, the stability of the reduced system is discussed as well. Finally, two numerical examples are provided to illustrate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

In this article, we discuss the time-domain dimension reduction methods for second-order systems by general orthogonal polynomials, and present a structure-preserving dimension reduction method for second-order systems. The resulting reduced systems not only preserve the second-order structure but also guarantee the stability under certain conditions. The error estimate of the reduced models is also given. The effectiveness of the proposed methods is demonstrated by three test examples. [ABSTRACT FROM AUTHOR]