Fractional-order derivative approximations in discrete-time control systems - Machado, J. A. Tenreiro (2016)
The theory of fractional calculus goes back to he beginning of the theory of differential calculus but its inherent complexity postponed the application of the associated concepts. in the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. in the area of automatic control preliminay work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. the algorithms and discrete-time implementation.