H₂ Optimal Model Reduction of Coupled Systems on the Grassmann Manifold

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.