Basic Control Theory for Linear Fractional Differential Equations With Constant Coefficients

In 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 present some simple examples, including a linear fractional harmonic oscillator, to illustrate our results. Moreover, another simple linear system of incommensurate fractional orders is suggested as an open problem.