离散系统的离散脉冲正交函数模型降阶方法（英文）

谢震; 唐升国; 王兆鸿

doi:10.13568/j.cnki.651094.651316.2023.12.13.0003

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离散系统的离散脉冲正交函数模型降阶方法（英文）

更新时间：2026-01-21

- 离散系统的离散脉冲正交函数模型降阶方法（英文）
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 41, Issue 6, Pages: 641-650(2024)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.12.13.0003
  CLC： O241.6
- Published：2024
- 稿件说明：
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[1]谢震,唐升国,王兆鸿.离散系统的离散脉冲正交函数模型降阶方法（英文）[J].新疆大学学报(自然科学版中英文),2024,41(06):641-650.
[1]谢震,唐升国,王兆鸿.离散系统的离散脉冲正交函数模型降阶方法（英文）[J].新疆大学学报(自然科学版中英文),2024,41(06):641-650. DOI： 10.13568/j.cnki.651094.651316.2023.12.13.0003.

DOI：10.13568/j.cnki.651094.651316.2023.12.13.0003.

摘要

针对离散线性和离散双线性系统

提出了基于离散脉冲正交函数的模型降阶方法.首先

将离散线性系统和离散双线性系统分别在离散脉冲正交函数所张成的空间中展开

得到两类关于系统状态变量展开系数的迭代关系式.然后

对所得两类迭代关系式分别实施修正的Arnoldi过程

得到正交投影矩阵

进而得到降阶系统.理论分析表明

所得降阶系统的输出变量能够匹配原始系统输出变量的有限个展开系数.最后

两个数值例子验证了所提模型降阶方法的可行性和有效性.

Abstract

This paper explores model order reduction(MOR) methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs). Firstly

the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs

and two recurrence formulas for the expansion coefficients of the system's state variables are obtained. Then

a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices

by which the reduced-order systems are obtained. Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system's output variables. Finally

two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

关键词

Keywords

references

蒋耀林．模型降阶方法[M]．北京：科学出版社，2010.JIANG Y L.Model order reduction methods[M].Beijing:Science Press,2010.(in Chinese)

PILLAGE L T,ROHRER R A.Asymptotic waveform evaluation for timing analysis[J].IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1990,9(4):352-366.

FREUND R W.Krylov-subspace methods for reduced-order modeling in circuit simulation[J].Journal of Computational and Applied Mathematics,2000,123(1/2):395-421.

MOORE B.Principal component analysis in linear systems:Controllability,observability,and model reduction[J].IEEE Transactions on Automatic Control,1981,26(1):17-32.

JIANG Y L,CHEN H B.Time domain model order reduction of general orthogonal polynomials for linear input-output systems[J].IEEE Transactions on Automatic Control,2012,57(2):330-343.

WANG Z H,JIANG Y L,XU K L.Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions[J].International Journal of Systems Science,2022,53(10):2045-2062.

WANG Z H,JIANG Y L,XU K L.Time domain and frequency domain model order reduction for discrete time-delay systems[J].International Journal of Systems Science,2020,51(12):2134-2149.

XU K L,JIANG Y L,LI Z,et al.Model reduction of discrete time-delay systems based on Charlier polynomials and high-order Krylov subspaces[J].Linear Algebra and Its Applications,2023,661:222-246.

WANG X L,JIANG Y L.Model reduction of discrete-time bilinear systems by a Laguerre expansion technique[J].Applied Mathematical Modelling,2016,40(13/14):6650-6662.

TANG S G,JIANG Y L,WANG Z H.Time domain model order reduction of discrete-time bilinear systems by discrete Walsh functions[J].International Journal of Control,2024,97(7):1500-1511.

HORNG I R,HO S J.Discrete pulse orthogonal functions for the analysis,parameter estimation and optimal control of linear digital systems[J].International Journal of Control,1987,45(2):597-605.

ROWLEY C W.Model reduction for fluids,using balanced proper orthogonal decomposition[J].International Journal of Bifurcation and Chaos,2005,15(3):997-1013.

ZHANG L Q,LAM J,HUANG B,et al.On gramians and balanced truncation of discrete-time bilinear systems[J].International Journal of Control,2003,76(4):414-427.

LEREDDE Y,LELLOUCHE J M,DEVENON J L,et al.On initial,boundary conditions and viscosity coefficient control for Burgers’ equation[J].International Journal for Numerical Methods in Fluids,1998,28(1):113-128.

BENNER P,BREITEN T,DAMM T.Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems[J].International Journal of Control,2011,84(8):1398-1407.

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