Abstract
In this paper, we discuss truncated Gramians (TGrams) for bilinear control systems and their relations to Lyapunov equations. We show how TGrams relate to input and output energy functionals, and we also present interpretations of controllability and observability of the bilinear systems in terms of these TGrams. These studies allow us to determine those states that are less important for the system dynamics via an appropriate transformation based on the TGrams. Furthermore, we discuss advantages of the TGrams over the Gramians for bilinear systems as proposed in Al-baiyat and Bettayeb (Proceedings of 32nd IEEE CDC, pp. 22–27, 1993). We illustrate the efficiency of the TGrams in the framework of model order reduction via a couple of examples, and compare to the approach based on the full Gramians for bilinear systems.
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Acknowledgements
The authors thank Dr. Stephen D. Shank for providing the MATLAB implementation to compute the low-rank solutions of the generalized Lyapunov equations.
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Benner, P., Goyal, P., Redmann, M. (2017). Truncated Gramians for Bilinear Systems and Their Advantages in Model Order Reduction. In: Benner, P., Ohlberger, M., Patera, A., Rozza, G., Urban, K. (eds) Model Reduction of Parametrized Systems. MS&A, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-58786-8_18
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DOI: https://doi.org/10.1007/978-3-319-58786-8_18
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