A Pseudo S-Plane Mapping of Z-Plane Root Locus

@article{Noury2020APS,
  title={A Pseudo S-Plane Mapping of Z-Plane Root Locus},
  author={Keyvan Noury and Bingen Yang},
  journal={Volume 7A: Dynamics, Vibration, and Control},
  year={2020}
}
In this paper, inspired by the geometric inversion transformation, a novel transformation of the z-plane root locus to a pseudo s-plane is proposed. In the z-plane, the stability of a discrete closed-loop system (a sampled-data control system) requires that all the system poles lie within the unit circle. In root locus analysis, the unit circle region seems congested, compared to the stability region of a continuous system, which is the left half of the s-plane. In the case of fast sampling…