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Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances

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Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yuri S. Ledyaev

  2. Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK

    Richard B. Vinter

Authors
  1. Yuri S. Ledyaev
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  2. Richard B. Vinter
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Correspondence to Yuri S. Ledyaev.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 268, pp. 2312–251.

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Ledyaev, Y.S., Vinter, R.B. Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances. Proc. Steklov Inst. Math. 268, 222–241 (2010). https://doi.org/10.1134/S0081543810010153

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