Canonical decomposition of linear time invariant fractional differential system

Using the differentiation and integration of fractional order or non-integer order in systems control is gaining more and more interests from the systems control community. In the present document, some important results are being provided on the linear time invariant fractional differential system. The specific case of uncontrollable and/or unobservable system is treated in a state-space form. The outcome is a proof that the results of this study are similar to ordinary differential system. A numerical example is presented here to illustrate the theoretical results.