Nonlinear model order reduction based on tensor Kronecker product expansion with Arnoldi process

In this paper, we present a model order reduction (MOR) method for large nonlinear input–output systems based on tensor Kronecker product expansion with Arnoldi process. We first approximate the nonlinear system with a quadratic form at single-point expansion, and then use a tensor Kronecker product analysis to it. Constructing the projection matrix through solving a linear equation, a reduced quadratic system is produced, which can match the first several expansion coefficients of the original output. What is more, it can preserve the stability and passivity under some certain conditions as well. The error estimation is also well discussed. Finally, the robust behavior of our MOR method is successfully illustrated via two numerical examples.