Fixed Point Transformations in the Adaptive Control of Fractional Order MIMO Systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lac...

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Detalhes bibliográficos
Autor principal: Tar, József K. (author)
Outros Autores: Rudas, Imre J. (author), Nádai, László (author), Kozłowski, Krzysztof R. (author), Machado, J. A. Tenreiro (author)
Formato: bookPart
Idioma:eng
Publicado em: 2009
Assuntos:
Texto completo:http://hdl.handle.net/10400.22/8842
País:Portugal
Oai:oai:recipp.ipp.pt:10400.22/8842
Descrição
Resumo:Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.