Abstract
We study a two dimensional system which is globally asymptotically stabilizable with a discontinuous feedback but for which there exists no smooth stabilizing feedback. However this asymptotic stability is not robust to measurement, actuator or external noise. We show that such a robustness property can be achieved with an hybrid controller. In doing so we need to introduce an appropriate notion of solutions for hybrid systems.
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© 2001 Springer-Verlag London Limited
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Prieur, C. (2001). A robust globally asymptotically stabilizing feedback: The example of the artstein’s circles. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110309
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DOI: https://doi.org/10.1007/BFb0110309
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