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.

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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.