SVD-Krylov based model reduction for time-varying periodic descriptor systems

Rahman, Ashfiqur; Hossain, Mohammad‐Sahadet

doi:10.1109/iceeict.2015.7307363

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…In order to validate our proposed model reduction approach we compare our results with the results of iterative rational Krylov algorithm (IRKA) [12,11], where the reduced-order model was obtained via the Krylov based multiple interpolations over the same data file used in this example [19].…”

Section: Numerical Resultsmentioning

confidence: 99%

Projection-based model reduction for time-varying descriptor systems: New results

Hossain¹

2016

NACO

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We have presented a Krylov-based projection method for model reduction of linear time-varying descriptor systems in [13] which was based on earlier ideas in the work of J. Philips [17] and others. This contribution continues that work by presenting more details of linear time-varying descriptor systems and new results coming from real fields of application. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding differential-algebraic equation. This is realized by orthogonal projection onto a rational Krylov subspace. The algorithmic realization of the method employs recycling techniques for shifted Krylov subspaces and their invariance properties. The proposed method works efficiently for macro-models, such as time varying circuit systems and models arising in network interconnection, on limited frequency ranges. Bode plots and step response are used to illustrate both the performance and accuracy of the reduced-order model.

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Section: Numerical Resultsmentioning

confidence: 99%

Projection-based model reduction for time-varying descriptor systems: New results

Hossain¹

2016

NACO

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“…

Im false(W false) = span false[k_{j k + 1} false(A, B; σ_{k + 1} false) \dots k_{j 2 k} false(A, B; σ_{2 k} false) false]

, then

j_{k}

number of moments match between the transfer functions of the original and reduced order model at the interpolation point

σ_{k}

for

k = 1, . . ., 2 K

. For more information, we refer to [39] and the references therein.…”

Section: Model Reduction Strategiesmentioning

confidence: 99%

Comparative analysis of model reduction strategies for circuit based periodic control problems

Hossain

Tahsin

Omar

et al. 2020

Asian Journal of Control

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This paper is a comparative analysis of two prominent iterative algorithms for model order reduction of linear time‐varying (LTV) periodic systems where the system's matrices are singular. Our proposed method is based on a reformulation of the LTV model to an equivalent linear time‐invariant (LTI) model using a suitable discretization procedure. The resulting LTI model is reduced in two ways, once by applying a balanced truncation method and once by applying a Krylov‐based method known as iterative rational Krylov algorithm (IRKA). During the application of balanced truncation, the low‐rank Cholesky factorized alternating directions implicit (LRCF‐ADI) method is used to estimate the solutions of the corresponding LTI form of Lyapunov equations. Since the system's matrices are singular, the concept of pseudo‐inverse is adopted to compute the shift parameters needed in the LRCF‐ADI iterations. For the Krylov‐based IRKA, our work is twofold. We solve the time‐invariant Lyapunov equation for the observability Gramian and apply a moment‐matching Krylov technique. The accuracy and effectiveness of the two proposed techniques are demonstrated with the help of frequency response graphs, bode plots, and eigenstructure of the main and reduced models.

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A structured Krylov subspace approach based model reduction of periodic control system in lifted form

Hossain

Chowdhury

Rahman

2021

2021 6th International Conference on Inventive Computation Technologies (ICICT)

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SVD-Krylov based model reduction for time-varying periodic descriptor systems

Cited by 3 publications

References 26 publications

Projection-based model reduction for time-varying descriptor systems: New results

Projection-based model reduction for time-varying descriptor systems: New results

Comparative analysis of model reduction strategies for circuit based periodic control problems

A structured Krylov subspace approach based model reduction of periodic control system in lifted form

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