`p-equivalence of Discretizations of Analog Controllers ?

This paper first introduces the fractional-order hold transformation that, together with the generalized bilinear transformation recently proposed in Zhang et al. [2007], contains all commonly used discretization methods as special cases. In light of this, it further shows that at fast sampling, all the digital approximations of an analog controller are equivalent in the sense of `p induced norm for p ∈ [1,∞] when the analog controller is stable or in the sense of some gap metric even when it is unstable.