Extended balancing of continuous LTI systems: a structure-preserving approach
Borja Rosales, L.P. (TU Delft Learning & Autonomous Control)
Scherpen, Jacquelien M.A. (Rijksuniversiteit Groningen)
Fujimoto, Kenji (Kyoto University)
In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.
To reference this document use:
Linear matrix inequalities
Reduced order systems
IEEE Transactions on Automatic Control, 68 (1), 257-271
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© 2023 L.P. Borja Rosales, Jacquelien M.A. Scherpen, Kenji Fujimoto