A trust-region method for H ₂ model reduction of bilinear systems on the Stiefel manifold

This paper investigates the Riemannian trust-region method for H ₂ model reduction of bilinear systems. The H ₂ error norm is treated as a cost function on the Stiefel manifold such that the orthogonality constraint for the projection matrix is plainly satisfied. The property related to the Euclidean gradient is studied. Then, the inner product associated with the Riemannian Hessian is derived, which can simplify the expression of the trust-region subproblem. The trust-region method for H ₂ model reduction is accordingly established and the convergence is further discussed. Finally, two numerical examples are employed to demonstrate the performance of the proposed method.