Geodesic
Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances
Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 231-251

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We consider a nonlinear control system which, under persistently acting disturbances, can be asymptotically driven to the origin by some non-anticipating strategy with infinite memory (such a strategy determines a value of control $u(t)$ at moment $t$ using complete information on the prehistory of disturbances until moment $t$). We demonstrate that this property is equivalent to the existence of a robust stabilizing (possibly discontinuous) feedback $k(x)$. 
@article{TRSPY_2010_268_a14,
     author = {Yuri S. Ledyaev and Richard B. Vinter},
     title = {Discontinuous feedback in nonlinear control: {Stabilization} under persistent disturbances},
     journal = {Informatics and Automation},
     pages = {231--251},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a14/}
}
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Yuri S. Ledyaev; Richard B. Vinter. Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances. Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 231-251. http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a14/