**2. LTI continuous-time fractional-order modeling**

In the beginning, most of the works consecrated to the study of FOS focused on continuous-time representations. The continuous-time state-space FOS representation was introduced in [24, 37–40]. It has been employed in analysis of system performances. The solution of the state-space equation was derived by using the Mittag-Lefller function [41]. Next, the stability of FOS was investigated [42] and a condition based on the argument principle was established to guarantee the asymptotic stability of the fractional-order system. Further, the controllability and the observability properties have been defined and some algebraic criteria of these two properties have been derived in [43]. Another contribution to the analysis of the controllability and the observability with commensurate FOS modeled by fractional state-space equations is brought in [44].
