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Observer-Based Control Design for Switched Affine Systems and Applications to DC–DC Converters

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Abstract

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors’s knowledge, have not yet been applied to this problem. Finally, observers for DC–DC converters are designed and simulated as application examples.

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Notes

  1. Of course, \({\dot{\tilde{\mathbf{x}}}}=\mathbf{0}\). However, this will be maintained only for the sake of notation.

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Acknowledgments

The authors would like to thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the sponsoring this study.

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Authors and Affiliations

  1. Departamento de Eletro-Eletrônica (DAE-E), Instituto Federal de Educação, Ciência e Tecnologia de Mato Grosso (IFMT), Campus Cuiabá, Rua Zulmira Canavarros, 95, Centro Norte, Cuiabá, MT, 78005-200, Brazil

    Victor Leonardo Yoshimura

  2. Laboratório de Pesquisa em Controle (LPC), Departamento de Engenharia Elétrica, Faculdade de Engenharia, Univ Estadual Paulista (UNESP), Campus Ilha Solteira, Avenida José Carlos Rossi, Nº 1370, Ilha Solteira, SP, 15385-000, Brazil

    Edvaldo Assunção, Emerson Ravazzi Pires da Silva & Marcelo Carvalho Minhoto Teixeira

  3. Departamento de Eletrônica, Instituto Federal de Educação, Ciência e Tecnologia Catarinense (IFC), Campus Videira, Rodovia SC 135, Videira, SC, 89560-000, Brazil

    Edson Italo Mainardi Júnior

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  1. Victor Leonardo Yoshimura
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  2. Edvaldo Assunção
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  3. Emerson Ravazzi Pires da Silva
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  4. Marcelo Carvalho Minhoto Teixeira
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Correspondence to Victor Leonardo Yoshimura.

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Yoshimura, V.L., Assunção, E., da Silva, E.R.P. et al. Observer-Based Control Design for Switched Affine Systems and Applications to DC–DC Converters. J Control Autom Electr Syst 24, 535–543 (2013). https://doi.org/10.1007/s40313-013-0044-z

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  • DOI: https://doi.org/10.1007/s40313-013-0044-z

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