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.