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 respon se gain of sampled-data systems with their intersample behavior taken into account. The properties of the infinite-dimensional congruent transformatio n (i.e., the Schur complement arguments and the Sylvester law of inertia) p lay a key role in the derivation. Specifically, it is highlighted that coun ting up the numbers of the negative eigenvalues of self-adjoint operators i s 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-infinity problem, where the key role is played by the positivity of operators and the loop-shifting technique. The effectiveness of the derive d algorithm is demonstrated through a numerical example.