An -embedding model-order reduction approach for differential-algebraic equation systems

Abstract

In this article, we present a model-order reduction (MOR) approach for a large-scale linear differential-algebraic equation (DAE) system. This MOR approach is accomplished in two steps: First, by applying an ε-embedding method, we approximate a DAE system with an ordinary differential equation (ODE) system which has an artificial parameter ε. Next, we use the Krylov subspace and balanced truncation methods to reduce the resulting ODE system. Some important properties for linear systems, such as stability and passivity, have been analysed. The effectiveness of our approach is also successfully illustrated through numerical examples.

H2 Optimal Model Reduction of Coupled Systems on the Grassmann Manifold

“…For some existing references dealing with DAE systems, one can refer to [9,19,23]. Apart from these, [5] proposed the ε-embedding technique to transform a DAE system into an ODE system by embedding a small perturbation. Then some model reduction methods concerning ODE systems are adaptable to the embedding system.…”

“…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.…”

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

“…Then, our MOR approach which is firstly introduced in [16] is applied to the closed-loop system. Moreover, a structure-preserving method is also used to reduce the closed-loop system.…”

“…According to [20], the matrices V e and H satisfy the following relations: Let Oðe,sÞ ¼ jsjJCJ 2 JBJ 2 JðsEÀAÞ À1 J 2 =ð1ÀejsjJðsEÀAÞ À1 J 2 Þ and LðeÞ ¼ ðÂV eà À1 e V T e À I n ÞÂV re H r,rÀ1 ½0 Á Á Á 0 I p . From [16], the error JHðsÞÀH e ðsÞJ 2 can be estimated as JHðsÞÀH e ðsÞJ 2 rOðe,sÞðeJðsEÀAÞ À1 J 2 þ JW J 2 JðsẼ e Àà e Þ À1 J 2 JLðeÞJ 2 Þ:…”

Balanced truncation with ε‐embedding for coupled dynamical systems

“…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.…”