Relaxed and Hybridized Backstepping

@article{Shiromoto2013RelaxedAH,
  title={Relaxed and Hybridized Backstepping},
  author={Humberto Stein Shiromoto and Vincent Andrieu and Christophe Prieur},
  journal={IEEE Transactions on Automatic Control},
  year={2013},
  volume={58},
  pages={3236-3241}
}
In this technical note, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system is not globally asymptotically stable but a suitable attractor (strictly containing the origin) is practically asymptotically stable. A design method is suggested to build a hybrid feedback law combining a backstepping controller with a locally… 

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