Model-order reduction of coupled DAE systems via technique and Krylov subspace method

Jiang, Yao‐Lin; Chen, Chun-Yue; Chen, Hai-Bao

doi:10.1016/j.jfranklin.2012.09.004

Cited by 11 publications

(7 citation statements)

References 21 publications

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“…L ε, i = L i T ε, i . 5: end for 6: for j = k 1 + 1, k 1 + 2, …, k do 7: Solve the Lyapunov equations (27) and (28) for P j and Q j , respectively. 8: Implement Algorithm 1 to compute the transformation matrices W j , T j ∈ ℝ n j × q j .…”

Section: Balanced Truncation Of Subsystemsmentioning

confidence: 99%

“…In this section, two examples are used to illustrate the efficiency of the

ε

‐embedding balanced truncation method. We compare our method with the generalised balanced truncation method [34], the one‐sided Krylov subspace method [27] and the two‐sided Krylov subspace method [28]. Both examples are operated in Matlab R2010b.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…On the basis of the ε-embedding technique, Chen et al [27] proposed the block Arnoldi MOR method and the balanced truncation MOR method to reduce the differential-algebraic equation system. For the coupled system, Jiang et al [28] presented the ε-embedding one-sided and two-sided Arnoldi MOR algorithms for both the closed-loop system and the subsystems. In this paper, we further explore the ε-embedding balanced truncation method of coupled systems.…”

Section: Introductionmentioning

confidence: 99%

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Balanced truncation with ε‐embedding for coupled dynamical systems

Jiang

Chen

Yang

2018

IET Circuits, Devices & Systems

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The authors focus on exploring the ε-embedding balanced truncation method of coupled systems. First, the coupled system is converted into a closed-loop system. Then, the ε-embedding technique and the Cholesky factor-alternating direction implicit algorithm are introduced to establish the balanced truncation method. The error bound and the stability of the resulting reduced-order system are discussed. Furthermore, the proposed method is applied to reduce the order of each subsystem such that the original interconnected structure is preserved. The error bound and the stability of the corresponding reduced-order system are also investigated. Finally, two numerical examples are employed to demonstrate the efficiency of the proposed method.

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Section: Balanced Truncation Of Subsystemsmentioning

confidence: 99%

“…In this section, two examples are used to illustrate the efficiency of the

ε

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Balanced truncation with ε‐embedding for coupled dynamical systems

Jiang

Chen

Yang

2018

IET Circuits, Devices & Systems

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“…The embedding process is similar to the above, apart from applying T l and T r to transform the system (2.4) before embedding the perturbation ε [12].…”

Section: According To Lemma 1 and The Fact That (Sementioning

confidence: 99%

“…As we know, ODE systems have been explored extensively, while DAE systems relatively less. [5,12] indicated that by embedding a small perturbation in a DAE system, a corresponding ODE system can be obtained. Then these existing model reduction methods for ODE systems can be employed.…”

Section: Introductionmentioning

confidence: 99%

H2 Optimal Model Reduction of Coupled Systems on the Grassmann Manifold

Yang

Jiang

2017

Mathematical Modelling and Analysis

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In this paper, we focus on the H2 optimal model reduction methods of coupled systems and ordinary differential equation (ODE) systems. First, the ε-embedding technique and a stable representation of an unstable differential algebraic equation (DAE) system are introduced. Next, some properties of manifolds are reviewed and the H2 norm of ODE systems is discussed. Then, the H2 optimal model reduction method of ODE systems on the Grassmann manifold is explored and generalized to coupled systems. Finally, numerical examples demonstrate the approximation accuracy of our proposed algorithms.

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