Model order reduction of port-Hamiltonian systems with inhomogeneous initial conditions via approximate finite-time Gramians

Based on the approximate finite-time Gramians, this paper studies model order reduction method of port-Hamiltonian systems with inhomogeneous initial conditions. The approximate controllability and observability Gramians on the finite-time interval [T₁,T₂](0≤T₁<T₂<∞) can be obtained by the shifted Legendre polynomials and the reduced port-Hamiltonian system is constructed by the union of dominant eigenspaces. Since the port-Hamiltonian system is square, the cross Gramian on the time interval [T₁,T₂] can also be approximated by using the shifted Legendre polynomials. Then, the truncated singular value decomposition of the approximate finite-time cross Gramian is carried out to obtain the projection matrix. Finally, the proposed methods are verified by two numerical examples.