Optimal reduced-order approximation of fractional dynamical systems

This paper deals with the fractional approximation of systems by integer reduced models. This approximation does not assume any restriction since the considered system can be commensurate or non commensurate, scalar or multivariable. Two model reduction schemes, namely, balanced truncation and singular perturbation balanced truncation are applied. To show the performance of this reduction, the reduced model obtained is compared to the integer model having the same order obtained by direct approximation. Several fractional models, are then considered. The obtained results are encouraging and attractive especially for the purpose of simulation and control of multivariable fractional systems.