Circle criterion and boundary control systems in factor form: input-output approach

Grabowski, Piotr, and Callier, Frank. "Circle criterion and boundary control systems in factor form: input-output approach." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1387-1403. <http://eudml.org/doc/207561>.

@article{Grabowski2001,
abstract = {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.},
author = {Grabowski, Piotr, Callier, Frank},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {input-output relations; infinite-dimensional control systems; semigroups; boundary control; stabilization; well-posedness; transmission line; circle criterion; infinite-dimensional SISO systems},
language = {eng},
number = {6},
pages = {1387-1403},
title = {Circle criterion and boundary control systems in factor form: input-output approach},
url = {http://eudml.org/doc/207561},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Grabowski, Piotr
AU - Callier, Frank
TI - Circle criterion and boundary control systems in factor form: input-output approach
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 6
SP - 1387
EP - 1403
AB - 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.
LA - eng
KW - input-output relations; infinite-dimensional control systems; semigroups; boundary control; stabilization; well-posedness; transmission line; circle criterion; infinite-dimensional SISO systems
UR - http://eudml.org/doc/207561
ER -