Reduced Order Approximation of MIMO Fractional Order Systems

A new two-stage method for reduced integer order approximation of fractional multiple-input, multiple-output (MIMO) systems is proposed. In the first stage, the transfer function matrix (TFM)
$G_{f}(s)$
of the given fractional order MIMO system is obtained and an integer order approximate TFM
$R(s)$
is formed by applying an existing approximation method to each fractional order transfer function (FOTF) of
$G_{f}(s)$
. In the second stage, a reduced order state space model is formed. The system matrix of the reduced order system is constructed by selecting the dominant poles from the intermediate high integer order model R(s). The input and output matrices are found by matching approximate time moments and Markov parameters of the final reduced order model and the original system. The proposed method has been illustrated by an example.