Optimal parametrization approach of the diffusive representation of a non-integer order dynamical system

Diffusive representation approach allows to reduce a fractional order system to an integer order one. The diffusive representation approach is based on the choice of a slowly increasing geometric series. Thus, to obtain an accurate approximation of the fractional system, the first term and the common ratio of the geometric series should be suitably chosen. In this paper, the geometric series parametrization problem is formulated as an optimization one where the decision (optimization) variables are the initial term and the common ratio. The objective function is the distance between the fractional and the integer states. To demonstrates the effectiveness of the parametrization approach proposed, two applications examples are provided.