The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.
@article{bwmeta1.element.bwnjournal-article-amcv11i2p377bwm,
author = {Belozyorov, Vasiliy},
title = {On an invariant design of feedbacks for bilinear control systems of second order},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {377-389},
zbl = {1073.93526},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p377bwm}
}
Belozyorov, Vasiliy. On an invariant design of feedbacks for bilinear control systems of second order. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 377-389. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p377bwm/
[000] Bellman R. (1976): Introduction to the Theory of Matrices. -Moscow: Nauka, (in Russian).
[001] Belozyorov V.Ye. and Poddubnaya O.A. (2000): Algebraici analysis of a conditional stability of solutions of quadratic systems of the differential equations. - Problems of Control and Computer Science, No.2, pp.13-23, (inRussian).
[002] Borisenko S.D. and Kosolapov V.I. et al. (1988): A Stability of Processes for Continuous and Discrete Perturbations. -Kiev: Naukova Dumka, (in Russian). | Zbl 0708.34045
[003] Demidovich B.P. (1967): Lectures on the Mathematical Theory of Stability. - Moscow: Nauka, (in Russian). | Zbl 0155.41601
[004] Gantmacher F.R. (1990): The Theory of Matrices. - Chelsea: Chelsea PubCo. | Zbl 0085.01001
[005] Isidori A. (1995): Nonlinear Control Systems, 3rd Ed. - London: Springer. | Zbl 0878.93001
[006] Khalil H. (1995): Nonlinear Systems, 2nd Ed. -New York: Prentice Hall.
[007] Sibirsky K.S. (1982): Introduction to the Algebraic Theory of Invariants of Differential Equations. - Kishinev: Shtinica, (in Russian).
[008] Zubov V.I. (1974): Mathematical Methods of Studying Systems of Automatic Control. - Leningrad: Mashinostroyeniye, (in Russian).