ℋ2-norm of a class of fractional transfer functions suited for modeling diffusive phenomena

This paper focuses on the ℋ
₂
-norm of a class of implicit fractional order transfer functions well suited to describe input-output behaviour of diffusive systems. First, analytical expression of the ℋ
₂
-norm of this kind of transfer function is established. This result is then used to evaluate the quality of an integer order approximation of such an implicit fractional transfer function.