On zeros of pulse transfer functions of systems with first-order hold

The Hagiwara-Yuasa-Araki theorems (1993) on limiting zeros of the pulse transfer function of sampled-data systems with first-order holds are extended by stating that limiting intrinsic zeros can be expressed as exponential functions of continuous-time zeros, and by determining the accuracy of the asymptotic results for both the discretization and the intrinsic zeros when the sampling interval is small. Closed form formulae are derived that express both the degree of the principal term of Taylor expansion of the difference between the true zeros and limiting ones as a function of the relative degree of the underlying continuous-time system and the value of the corresponding coefficient itself