The paper starts from the suggestion of R. E. Kalman that additional informationon nonlinearity slope may improve the sufficient conditions for absolute stability. Thisleads to the so called systems with augmented dynamics. Motivated also by the problem ofthe PIO II aircraft oscillations - self sustained oscillations induced by the saturation nonlinearities,which are both sector and slope restricted - the paper considers a generalization ofthe Yakubovich criterion to the case of the systems with critical and unstable linear part. Thesame generalization concerns a quite well known stability criterion where only slope restrictionsare taken into account: the published version is improved by using all advantages of theLiapunov method and of the frequency domain stability inequalities. The results are illustratedby several applications.
@article{104,
title = {Systems with Monotone and Slope Restricted Nonlinearities},
journal = {Tatra Mountains Mathematical Publications},
volume = {49},
year = {2011},
doi = {10.2478/tatra.v48i0.104},
language = {EN},
url = {http://dml.mathdoc.fr/item/104}
}
Răsvan, Vladimir. Systems with Monotone and Slope Restricted Nonlinearities. Tatra Mountains Mathematical Publications, Tome 49 (2011) . doi : 10.2478/tatra.v48i0.104. http://gdmltest.u-ga.fr/item/104/