The 21st Century Systems: An Updated Vision of Discrete-Time Fractional Models

Two different approaches for describing discrete-time fractional linear systems are presented. The first is based on the nabla and delta discrete-time derivatives. In this case, suitable exponentials are introduced and used to define discrete Laplace transforms. The second approach is based on the bilinear (Tustin) transformations. For both cases, appropriate algorithms for obtaining the impulse, step, and frequency responses are presented. The state-variable representation is also analysed.

Automated summary

Two different approaches for describing discrete-time fractional linear systems are presented, one based on discrete derivatives and the other on bilinear transformations. Algorithms for obtaining impulse, step, and frequency responses are provided, along with analysis of state-variable representation.