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 /spl gamma/ > o and thus can be used as a basis for a bisection algorithm. Unlike all currently existing results, the proposed procedure requires the operator /spl gamma//sup 2/I - D /sub 11/D/spl breve//sub 11/* neither to be positive nor even to be invertible, thus eliminating unnecessary restrictions of the existing approaches (here D/spl breve//sub 11/ stands for the feedthrough term of the lifted system).