论文信息 - A robust globally asymptotically stabilizing feedback: The example of the artstein’s circles

A robust globally asymptotically stabilizing feedback: The example of the artstein’s circles

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.

Christophe Prieur | C. Prieur

[1] R. W. Brockett,et al. Asymptotic stability and feedback stabilization , 1982 .

[2] Eduardo Sontag. Stability and stabilization: discontinuities and the effect of disturbances , 1999, math/9902026.

[3] Z. Artstein. Stabilization with relaxed controls , 1983 .

[4] Yuandan Lin,et al. A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .

[5] J. Hale,et al. Stability of Motion. , 1964 .

[6] Yu. S. Ledyaev,et al. Asymptotic controllability implies feedback stabilization , 1997, IEEE Trans. Autom. Control..

[7] Christophe Prieur. Uniting Local and Global Controllers with Robustness to Vanishing Noise , 2001, Math. Control. Signals Syst..

[8] E. P. Ryan,et al. Discontinuous Feedback and Universal Adaptive Stabilization , 1990 .

[9] L. Praly,et al. Uniting local and global controllers , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10] L. Tavernini. Differential automata and their discrete simulators , 1987 .

[11] Eduardo Sontag. Clocks and insensitivity to small measurement errors , 1999 .

[12] Yu. S. Ledyaev,et al. A Lyapunov characterization of robust stabilization , 1999 .