Balanced truncation with ε‐embedding for coupled dynamical systems

Abstract

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.

Structure preserving model reduction of second‐order time‐delay systems via approximate Gramians

“…As can be seen, when the damping matrix is singular, the system (3) cannot be converted into the system (4). In order to circumvent this case, we apply the ‐embedding technique [8, 9] to the system (3) with the singular damping matrix .…”

“…Concerning the differential algebraic equation (DAE) system, Chen , et al [8] proposed the ‐embedding technique, which converted a DAE system into an ordinary differential equation (ODE) system such that some MOR methods suitable for ODE systems can be applicable to DAE systems. In addition, Jiang , et al [9] explored the balanced truncation associated with the ‐embedding technique for the coupled system with DAE subsystems.…”