Model Reduction of Nonlinear Systems by Trajectory Piecewise Linear Based on Output-Weighting Models: A Balanced-Truncation Methodology

Abstract

This paper extends some methods in model order reduction (MOR) of nonlinear models by trajectory piecewise-linear models based on output weighting (TPWLOW). The devised methods generalize the balanced-truncation method as the core for the proposed algorithms. These algorithms preserve the stability in some mentioned conditions. An error bound of reduction is calculated for these algorithms. In addition, a Krylov–TBR combinational MOR is also casted which benefits from the advantages of both balanced-truncation and Krylov subspace methods. The results show that in balanced-truncation-based algorithms, the efficiency of the first proposed algorithm fairly exceeds the second one. In addition, it is shown that the Krylov–TBR algorithm can reach the same efficiency despite remarkable lower order, provided that the designer can find a stable subspace. The robustness of TPWLOW-reduced models to linearization point movement is also evaluated, which shows the less sensitivity of the proposed methods in comparison with formerly introduced trajectory piecewise-linear models.