Abstract
This chapter analyzes performance limitations and stability robustness of the unity feedback configuration of Figure 12.2 considered in Chapter 12. We use the material on nonlinear operator theory developed in §12.1.1 of Chapter 12.
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Notes and References
Sensitivity Limitations
The results on nonlinear Lipschitz sensitivity limitations are based on Seron & Goodwin (1996), Seron (1995) and Goodwin & Seron (1995).
The nonlinear extension of the water-bed effect is due to Shamma (1991).
Stability Robustness
§13.5 is based on Seron & Goodwin (1996). Robustness tests similar to those given in §13.5 were obtained by Astolfi & Guzzella (1993) using the L2-gain (or “nonlinear H∞ norm”) in lieu of the Lipschitz constant. Astolfi & Guzzella, however, used a state-space approach. Other results on robustness for nonlinear feedback systems are the works of Georgiou & Smith (1995a, 1995b, 1995c), who use a nonlinear generalization of the gap metric.
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© 1997 Springer-Verlag London Limited
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Seron, M.M., Braslavsky, J.H., Goodwin, G.C. (1997). Nonlinear Control. In: Fundamental Limitations in Filtering and Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0965-5_13
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DOI: https://doi.org/10.1007/978-1-4471-0965-5_13
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1244-0
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