Bisection algorithm for computing the frequency response gain of sampled-data systems - infinite-dimensional congruent transformation approach

This paper derives a bisection algorithm for computing the frequency response gain of sampled-data systems with their intersample behavior taken into account. The properties of the infinite-dimensional congruent transformation (i.e., the Schur complement arguments and the Sylvester law of inertia) play a key role in the derivation. Specifically, it is highlighted that counting up the numbers of the negative eigenvalues of self-adjoint operators is quite important for the computation of the frequency response gain. This contrasts with the well-known arguments on the related issue of the sampled-data H_∞ problem, where the key role is played by the positivity of operators and the loop-shifting technique. The effectiveness of the derived algorithm is demonstrated through a numerical example