Piecewise Polynomial Model Reduction Method for Nonlinear Systems in Time Domain

Model order reduction (MOR) of nonlinear systems draws great attention in the past several decades. This paper presents a new MOR method in time domain for nonlinear dynamical systems. The new algorithm is based on the combination of the Taylor series expansion for the state variable x(t) and the trajectory piecewise polynomial technique. Firstly, the nonlinear system is approximated by a piecewise polynomial representation. Then, based on the Taylor series coefficients of x(t), we formulate the projection matrix V for the piecewise polynomial system and the compact model of the piecewise polynomial system is obtained in the following. Besides, error estimation and stability analysis are also presented in this paper. Finally, two nonlinear systems are tested to verify the effectiveness of the algorithm.