Model reduction by differential balancing based on nonlinear Hankel operators

Kawano, Y. & Scherpen, J. M. A., Jul-2017, In : IEEE Transactions on Automatic Control. 62, 7, 16 p.

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In this paper, we construct balancing theory for nonlinear systems in the contraction framework. First, we define two novel controllability and observability functions via prolonged systems. We analyze their properties in relation to controllability and observability, and use them for so-called differential balancing, and its application to model order reduction. One of the main contribution of this paper is showing that differential balancing has close relationships with the Frechet derivative of the nonlinear Hankel operator. Inspired by [3], we provide a generalization in order to have a computationally more feasible method. Moreover, error bounds for model reduction by generalized balancing are provided.
Original languageEnglish
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number7
Publication statusPublished - Jul-2017


  • Reduced order systems, Controllability, Trajectory, Observability, Nonlinear systems, Stability analysis, Time-varying systems

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