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A Dynamic-State Feedback Approach Employing a New State-Space Description for the Fast Wavelet Transform with Multiple Decomposition Levels

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Abstract

This research paper proposes a wavelet-based dynamic-state feedback control strategy in the discrete time domain. In this proposal, the state feedback employs a state-space description for the fast wavelet transform, which is also developed in this article. The feedback gains are obtained through a linear quadratic regulator formulation, with cost weights adjusted according to suitable performance metrics. This proposal brings forward efficient results, as well as more robust systems to external perturbations and sensor noises.

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Notes

  1. The mentioned values should be avoided because they have null sine or cosine values, which would correspond to zero-valued elements in the controllability and observability matrices. Therefore, the resulting matrices would not have full rank.

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Acknowledgements

The authors acknowledge the support of the Brazilian agencies CAPES, CNPq (research fellowships and Ph.D. Grant 160545/2013-7) and FAPESP (Grant 2011/17610-0).

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Authors and Affiliations

  1. São Paulo State University (Unesp), School of Engineering, Ilha Solteira, São Paulo, Brazil

    J. C. Uzinski & E. Assunção

  2. Institute of Science and Technology (ICT), Universidade Federal de São Paulo - UNIFESP, São José dos Campos, São Paulo, Brazil

    H. M. Paiva

  3. Department of Electronic Engineering - ITA, São José dos Campos, São Paulo, Brazil

    R. K. H. Galvão

  4. Department of Mathematics - UEMS, Universidade Estadual de Mato Grosso do Sul, Cassilândia, Mato Grosso do Sul, Brazil

    M. A. Q. Duarte

  5. Department of Mathematics - FEIS, Universidade Estadual Paulista - UNESP, Ilha Solteira, São Paulo, Brazil

    F. Villarreal

Authors
  1. J. C. Uzinski
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  2. H. M. Paiva
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  3. R. K. H. Galvão
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  4. E. Assunção
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  5. M. A. Q. Duarte
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  6. F. Villarreal
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Correspondence to J. C. Uzinski.

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Uzinski, J.C., Paiva, H.M., Galvão, R.K.H. et al. A Dynamic-State Feedback Approach Employing a New State-Space Description for the Fast Wavelet Transform with Multiple Decomposition Levels. J Control Autom Electr Syst 28, 303–313 (2017). https://doi.org/10.1007/s40313-017-0312-4

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  • DOI: https://doi.org/10.1007/s40313-017-0312-4

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