H₂ Optimal Model Reduction of Coupled Systems on the Grassmann Manifold

Abstract

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.

Keywords:

• model reduction
• H₂ optimality
• coupled systems
• manifolds

AMS Subject Classification:

• 78M34
• 14M15

Additional information

Funding

This work was supported by the Natural Science Foundation of China (Grant Nos. 61663043 and 11371287) and the Doctoral Innovation Project of Xinjiang University (Grant No. XJUBSCX-2016005).