Minimal Realizations for Some Classes of Fractional Order Transfer Functions

It has been known that finding a minimal pseudo state space realization for a fractional order transfer function is helpful in circuitry implementation of such a transfer function with the minimum number of fractional capacitors. Considering this importance, the present paper deals with finding minimal realizations for some classes of fractional order transfer functions. To this end, at first some upper bounds are obtained for the minimal inner dimension of a fractional order transfer function. By considering these upper bounds and also the lower bounds, previously presented in literature, the minimal inner dimension is exactly found for some classes of fractional order transfer functions. Moreover, the minimal realizations for these classes are also suggested.