No abstract

In this work, the regulation problem is extended to the field of fractional-order linear systems considering the Caputo fractional derivative. The regulation equations are obtained on the basis of the Francis equations. It is also shown that the linear fractional regulator exists at t = 0 only if the order of the plant is not greater than the order of the reference system.Takagi-Sugeno fuzzy models, adaptive neuro-fuzzy inference system, and generic algorithm. In those works, the involvement of nonlinear partial differential equations is avoided.On the other hand, fractional-order differential equations have been proven to be of great help during the modeling of real physics processes [10,11]. As consequence, the extension of integer-order results to the * Correspondence: jmedac@ipn.mx This work is licensed under a Creative Commons Attribution 4.0 International License.