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Discontinuous feedback in nonlinear control: stabilization under persistent disturbances. (English. Russian original) Zbl 1201.93050

Proc. Steklov Inst. Math. 268, 222-241 (2010); translation from Trudy Mat. Inst. Steklova 268, 231-251 (2010).
Summary: 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 \(k(x)\).

MSC:

93B52 Feedback control
93D15 Stabilization of systems by feedback
93C73 Perturbations in control/observation systems
93C10 Nonlinear systems in control theory
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References:

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