The L^{P} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^{P} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.
@article{bwmeta1.element.bwnjournal-article-amcv13i2p179bwm,
author = {Gurfil, Pini},
title = {Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {13},
year = {2003},
pages = {179-184},
zbl = {1050.93057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p179bwm}
}
Gurfil, Pini. Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 179-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p179bwm/
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