A circle criterion is obtained for a SISO Lur’e feedback control system consist- ing of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previ- ously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the trans- fer function belongs to H∞ (Π+ ) and satisfies a frequency-domain inequality of the circle criterion type. We also require that the closed-loop system be well- posed, i.e. for any initial state x0 ∈ H the truncated input and output sig- nals uT , yT belong to L2 (0, T ) for any T > 0. The technique of the proof adapts Desoer-Vidyasagar’s circle criterion method (Desoer and Vidyasagar, 1975, Ch. 3, Secs. 1 and 2, pp. 37–43, Ch. 5, Sec. 2, pp. 139–142 and Ch. 6, Secs. 3 and 4, pp. 172–174), and uses the input-output map developed by the authors (Grabowski and Callier, 2001). The results are illustrated by two trans- mission line examples: (a) that of the loaded distortionless RLCG type, and (b) that of the unloaded RC type. The conclusion contains a discussion on improving the results by the loop-transformation technique.
@article{bwmeta1.element.bwnjournal-article-amcv11i6p1387bwm,
author = {Grabowski, Piotr and Callier, Frank},
title = {Circle criterion and boundary control systems in factor form: input-output approach},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {1387-1403},
zbl = {0999.93061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i6p1387bwm}
}
Grabowski, Piotr; Callier, Frank. Circle criterion and boundary control systems in factor form: input-output approach. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 1387-1403. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i6p1387bwm/
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