Model Reduction of Large Scale Descriptor Systems Using Time Limited Gramians

Haider, Khawaja Shafiq; Ghafoor, Abdul; Imran, Muhammad; Malik, Fahad Mumtaz

doi:10.1002/asjc.1444

Cited by 33 publications

(22 citation statements)

References 25 publications

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“…For this reason, research works which aim to obtain a balanced system in a numerically efficient way have still been carried out (see e.g. [44][45][46][47][48][49][50][51][52]). The preliminary results of approximation of a fractional-order system by use of the expanded state space model and the BT method have been presented in [33].…”

Section: Resultsmentioning

confidence: 99%

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Rydel

Stanisławski

2019

Asian Journal of Control

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This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer-order approximator to linear time-invariant discrete-time noncommensurate fractional-order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete-time fractional-order systems by means of a high integer-order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low-dimension fractional-order systems and high implementation lengths.

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Section: Resultsmentioning

confidence: 99%

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Rydel

Stanisławski

2019

Asian Journal of Control

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“…Substitution of the above equations in (26), satisfies (24). Now, after substitution of matricesC ss ,D o , andB o in (25), we havē…”

Section: Proposed Fwohna Algorithmmentioning

confidence: 99%

“…Later, Imran et al [20] presented an improvement of [11] by considering a similar effect on the eigenvalues of symmetric matrices. Some recent developments on model reduction are appeared in [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction

Kumar

Sreeram

2019

Asian Journal of Control

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In this paper, we present frequency‐weighted optimal Hankel‐norm model reduction algorithms for linear time‐invariant continuous‐time systems by representing an original higher‐order system into new fictitious systems. The new system representations are derived through factorization of the resulting sub‐matrices that are obtained after transformations. As the proposed approaches are factorization dependent, additional results with both approaches are included using another factorization of the fictitious input–output and weight matrices. The proposed algorithms generate stable reduced models with double‐sided weights and provide a substantial improvement in the weighted error. A numerical example is given to compare the efficacy of the proposed algorithms with the well‐known frequency‐weighted techniques.

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“…The frequency weighted (FW) methods are extended versions of BT. They are based on either (1) direct application of input/output weighting functions [16,29,63,66,68] or (2) Gramians in a restricted frequency interval = [ω 1 , ω 2 ] in the frequency domain [5,10,22,28,31] or (3) Gramians in a restricted time interval τ = [t 1 , t 2 ] in the time domain [22,25,32,61]. These lead to a higher model accuracy in selected frequency ranges, in particular when the parameters of the weighting functions and frequency/time intervals are optimized [50].…”

Section: Introductionmentioning

confidence: 99%

New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

Rydel

2018

Adv Comput Math

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This paper presents a new approach to modeling of linear time-invariant discrete-time non-commensurate fractional-order single-input single-output state space systems by means of the Balanced Truncation and Frequency Weighted model order reduction methods based on the cross Gramian. These reduction methods are applied to the specific rational (integer-order) FIR-based approximation to the fractional-order system, which enables to introduce simple, analytical formulae for determination of the cross Gramian of the system. This leads to significant decrease of computational burden in the reduction algorithm. As a result, a rational and relatively low-order state space approximator for the fractional-order system is obtained. A simulation experiment illustrates an efficiency of the introduced methodology in terms of high approximation accuracy and low time complexity of the proposed method.

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Model Reduction of Large Scale Descriptor Systems Using Time Limited Gramians

Cited by 33 publications

References 25 publications

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction

New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

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