On projection-based algorithms for model-order reduction of interconnects

Wang, J.M.; Chu, Chia-Chi; Yu, Qingbo; Kuh, E.S.

doi:10.1109/tcsi.2002.804542

Cited by 76 publications

(39 citation statements)

References 29 publications

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“…They suggest to use a subset of the approximated poles as interpolation points. Another interesting method for interpolation point selection in the area of circuits and systems is related to series expansions based on orthonormal polynomials, such as Chebyshev polynomials, and to series expansions based on generalised orthonormal basis functions in Hilbert and Hardy spaces [38].…”

Section: Adaptive Schemes For the Rational Methodsmentioning

confidence: 99%

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

Frangos

Jaimoukha

2008

European Journal of Control

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The Arnoldi and Lanczos algorithms, which belong to the class of Krylov subspace methods, are increasingly used for model reduction of large scale systems.The standard versions of the algorithms tend to create reduced order models that poorly approximate low frequency dynamics. Rational Arnoldi and Lanczos algorithms produce reduced models that approximate dynamics at various frequencies. This paper tackles the issue of developing simple Arnoldi and Lanczos equations for the rational case. This allows a simple error analysis to be carried out for both algorithms and permits the development of computationally efficient model reduction algorithms, where the frequencies at which the dynamics are to be matched can be updated adaptively.

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Section: Adaptive Schemes For the Rational Methodsmentioning

confidence: 99%

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

Frangos

Jaimoukha

2008

European Journal of Control

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“…The precision of the low order approximate model is of great importance since it determines whether the controller design is good or not. In the past few decades, significant research studies on model reduction have been reported, such as Krylov Subspace method [4], Pade approximation method [5] Shi'ang Qi is with the School of Huazhong University of Science and Technology, Hubei 430074, China (e-mail:15801299065@qq.com) approximation method [6], Dominant Poles method, Continued Fraction method [7], Gradual Waveform estimation method [8], Balance order reduction method, and so on. Though all these methods are suitable for linear systems, they are not useful to non-linear system.…”

Section: Introductionmentioning

confidence: 99%

Model Approximate Method of Complex System

Chen¹

2015

IJMO

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Abstract-During the internal model control of multivariate multiple time delay system, process model is very important in the design of controller, but complicated mathematical model is often encountered in decoupled multivariable multiple time delay system and needs to be reduced order. So this paper proposes a low order identification structure and an optimization method for model approximation of the complex model containing the time delay and non-minimum phase parts. In this paper, with the adoption of Pade approximation, a suboptimal approximate algorithm is used for the model approximation and model identification. The integral square error index and the frequency-domain integral square error index, as well as the integral time absolute error index is used to evaluate the approximate model comprehensively. Simulation results show that using the proposed model identification structure and adopting the suboptimal approximate algorithm to deal with this kind of approximation, that can get an approximate model that well reveals the dynamic characteristics of system and has a high approximation precision.Index Terms-Model approximation, complicated model, suboptimal approximate algorithm, error performance index.

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“…It is well established that model reduction techniques with preservation of passivity mostly belong to the balanced truncation class [11][12][13] or are spectral interpolation-based methods [14][15][16]. In the case of projection-based Krylov methods the problem of preservation of passivity has been studied by several researchers; for an overview of existing approaches see [6,[17][18][19][20][21]. The problem with the Krylov-based passivity preserving methods is that they often assume a special descriptor state space setting that may not always be feasible [11].…”

Section: Introductionmentioning

confidence: 99%

Model order reduction with preservation of passivity, non-expansivity and Markov moments

Knockaert

Dhaene

Ferranti

et al. 2011

Systems & Control Letters

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A new model order reduction (MOR) technique is presented which preserves passivity and non-expansivity. It is a projection-based method which exploits the solution of Linear Matrix Inequalities (LMI's) to generate a descriptor state space format which preserves positive-realness and bounded-realness. In the case of both non-singular and singular systems, solving the LMI can be replaced by equivalently solving an algebraic Riccati equation (ARE), which is known to be a more efficient approach. A new ARE and a frequency inversion technique are also presented to specifically deal with the important singular case. The preservation of Markov moments is also guaranteed by the judicious choice of a projection matrix.

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On projection-based algorithms for model-order reduction of interconnects

Cited by 76 publications

References 29 publications

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

Model Approximate Method of Complex System

Model order reduction with preservation of passivity, non-expansivity and Markov moments

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