Abstract:
In this work, the resolution of the fractional state space equation
representing the linear fractional systems of commensurate order, for all the eigenvalues types of
the state matrix A and the order of differentiation m was proposed. The explicit expressions of the
homogeneous and non-homogeneous solutions of this fractional state space equation were
developed. For different values of the state-space matrix A eigenvalues and the order m, the
obtained solutions are linear combinations of suitable fractional fundamental functions whose
Laplace transforms are irrational functions. The approximations of these irrational functions by
rational functions were obtained so that the solutions of the fractional state space equation are
linear combinations of classical exponential, cosine, sine, damped cosine and damped sine
functions. Illustrative examples for all the eigenvalues types of the state matrix A and the order m
were presented and the results obtained were very satisfactory.
