Balancing for nonlinear systems
Systems & Control Letters
Robust and optimal control
Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis
Nonlinear Analysis: Theory, Methods & Applications - 1st Level Done by Prameela
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Balanced realizations near stable invariant manifolds
Automatica (Journal of IFAC)
Model reduction for nonlinear systems with incremental gain or passivity properties
Automatica (Journal of IFAC)
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This paper discusses balanced realization and model order reduction for both continuous-time and discrete-time general nonlinear systems based on singular value analysis of the corresponding Hankel operators. Singular value analysis clarifies the gain structure of a given nonlinear operator. Here it is proved that singular value analysis of smooth Hankel operators defined on Hilbert spaces can be characterized by simple equations in terms of their states. A balanced realization and model order reduction procedure is derived based on it, and several important properties such as stability, balanced form, Hankel norm, controllability, and observability of the original system are preserved. The work improves the earlier results of [K. Fujimoto and J. M. A. Scherpen, IEEE Trans. Automat. Control, 50 (2005), pp. 2-18] and then continues with new balancing and model reduction results.