Buedo Fernández, SebastiánNieto Roig, Juan José2021-08-032021-08-032020Buedo-Fernández S and Nieto JJ (2020) Basic Control Theory for Linear Fractional Differential Equations With Constant Coefficients. Front. Phys. 8:377. doi: 10.3389/fphy.2020.00377http://hdl.handle.net/10347/26670In this paper we present an analogous result of the famous Kalman controllability criterion for first order linear ordinary differential equations with constant coefficients that applies to the case of linear differential equations of fractional order with constant coefficients. We use the fractional Gramian matrix, the range space and the Kalman matrix as main tools to derive a sufficient and necessary condition for the controllability of the fractional system. Moreover, we provide some simple examples, including a linear fractional harmonic oscillator, to illustrate our results. Finally, several open problems arising from this topic are suggested, including another simple linear system of incommensurate fractional ordersengCopyright © 2020 Buedo-Fernández and Nieto. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these termshttp://creativecommons.org/licenses/by/4.0/Linear differential equationsControllabilityFractional GramianFractional Differential EquationsKalman Matrixjournal article10.3389/fphy.2020.003772296-424Xopen access