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How mild can slow controls be?

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Abstract

For a linear control system, if a state can be steered to zero in some time, then it can be steered to zero in any larger time and it is expected that, as the time grows, the norm of the corresponding control to be smaller. We study here the behavior of the minimum \(L^p\)-control, \(p\in (1,+\infty ]\), as time duration goes to infinity.

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Acknowledgments

The research was supported by ID PNII-CT-ERC-2012 1, “Interconnected Methods to Analysis of Deterministic and Stochastic Partial Differential Equations”, project number 1ERC/02.07.2012.

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Authors and Affiliations

  1. Department of Mathematics, University Al. I. Cuza, 700506 , Iaşi, Romania

    O. Cârjă & A. I. Lazu

  2. Department of Mathematics, Octav Mayer Mathematics Institute, Romanian Academy, 700505 , Iaşi, Romania

    O. Cârjă

  3. Department of Mathematics, Gh. Asachi Technical University, 700506 , Iaşi, Romania

    A. I. Lazu

Authors
  1. O. Cârjă
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  2. A. I. Lazu
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Correspondence to O. Cârjă.

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Cârjă, O., Lazu, A.I. How mild can slow controls be?. Math. Control Signals Syst. 26, 547–562 (2014). https://doi.org/10.1007/s00498-014-0129-7

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  • DOI: https://doi.org/10.1007/s00498-014-0129-7

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