Frequency response of sampled-data systems

This paper introduces the concept of frequency response for sampled-data systems, and explores some basic properties as well as its computational procedures. It is shown that i) by making use of the lifting technique the notion of frequency response can be naturally introduced to sampled-data systems in spite of their time-varying characteristics, ii) it represents a frequency domain steady state behavior, iii) and it is also closely related to the original transfer function representation via an integral formula. It is shown that the computation of the frequency response can be reduced to a finite-dimensional eigenvalue problem, and some examples are presented to illustrate the results. Keywords— Sampled-data systems, Frequency response, Steady-state response, Gain computation problem.