Reduction theorems for stability of closed sets with application to backstepping control design

@article{ElHawwary2013ReductionTF,
  title={Reduction theorems for stability of closed sets with application to backstepping control design},
  author={Mohamed I. El-Hawwary and Manfredi Maggiore},
  journal={Automatica},
  year={2013},
  volume={49},
  pages={214-222}
}
We present a solution to the following reduction problem for asymptotic stability of closed sets in nonlinear systems. Given two closed, positively invariant subsets of the state space of a nonlinear system, Γ1 ⊂ Γ2, assuming that Γ1 is asymptotically stable relative to Γ2, find conditions under which Γ1 is asymptotically stable. We also investigate analogous reduction problems for stability and attractivity. We illustrate the implications of our results on the stability of sets for cascade… CONTINUE READING
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