Further study on the bisection algorithm for the frequency response gain computation of sampled-data systems and related issues

The authors (1998), derived a sophisticated bisection algorithm for computing the frequency response gain of sampled-data systems with the lifting approach. In this paper, we first give an alternative bisection method with the FR-operator approach, by applying the same fundamental technique as in the lifting case. Next, we clarify the relationship between the lifting-based bisection method and the one-dimensional search method given by Yamamoto and Khargonekar (1996). We then study the computational aspects of the frequency response gain of sampled-data systems, by comparing these three methods through a numerical example.