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

• Published in: IEEE transactions on automatic control Vol. 46; no. 3; pp. 369 - 381
• Main Authors: Ito, Y., Hagiwara, T., Maeda, H., Araki, M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2001; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Communication system control; Computation; Control systems; Control theory; Derivation; Digital control; Eigenvalues; Eigenvalues and eigenfunctions; Frequency response; Gain; Helium; Indium tin oxide; Operators; Robust stability; Sampling methods; Transformations
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.911415

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/sub /spl infin// 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.