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

Tar, József K.; Rudas, Imre J.; Nádai, László; Kozłowski, Krzysztof R.; Machado, J. A. Tenreiro

http://hdl.handle.net/10400.22/8842

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Authors

Tar, József K.

Rudas, Imre J.

Nádai, László

Kozłowski, Krzysztof R.

Machado, J. A. Tenreiro

Abstract(s)

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.