On balanced realization and finite-dimensional approximation for infinite-dimensional nonlinear systems

In this paper, we propose a finite-dimensional approximation for a nonlinear infinite-dimensional system via balanced realization. The proposed method is accomplished by balanced realization and singular value analysis for nonlinear systems. This approach is expected to derive effective approximate models preserving particular input-output behavior. Necessary and sufficient conditions characterizing balanced realization for infinite-dimensional systems are derived. Furthermore, the effectiveness of the proposed method is shown by a numerical simulation.