Computation of the frequency-response gain of sampled-data systems via projection in the lifted domain

This note addresses the computation of the frequency-response gain of sampled-data systems with their intersample behavior taken into account. The proposed method is based upon a novel necessary and sufficient condition for the frequency-response gain to be less than a given γ > o and thus can be used as a basis for a bisection algorithm. Unlike all currently existing results, the proposed procedure requires the operator γ²I - D ₁₁D˘₁₁* neither to be positive nor even to be invertible, thus eliminating unnecessary restrictions of the existing approaches (here D˘₁₁ stands for the feedthrough term of the lifted system).