| Title | Stabilization of some class of nonlinear systems that are uncontrollable the first approximation |
| Publication Type | Journal Article |
| Year of Publication | 2014 |
| Authors | Korobov, VI, Bebiya, MO |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2014.02.020 |
| Issue | 2 |
| Section | Mathematics |
| Pagination | 20-25 |
| Date Published | 2/2014 |
| Language | Russian |
| Abstract | The problem of stabilization for systems of the form $\dot x_{1}=u$, $ \dot x_{i}=x_{i-1}+f_{i-1}(t,x_{1},\ldots,x_{n})$, $ \dot x_{n}=x^{2k+1}_{n-1}+f_{n-1}(t,x_{1},\ldots,x_{n}) $, $i=\overline{2,n-1}$, that are uncontrollable in the first approximation is considered. The sufficient condition of existence of a quadratic Lyapunov function is obtained, and a method of construction of the Lyapunov function and the stabilizing control is described.
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| Keywords | nonlinear systems, stabilization, uncontrol |
1. Korobov V. I. Method of control function. Moscow; Izhevsk: NITs “Reguliatornaia i khaoticheskaia dinamika”, 2007 (in Russian).
2. Savchenko A. Ya., Ignatev A. O. Some stability problems for nonautonomous dynamical systems. Kyiv: Nauk. dumka, 1989 (in Russian).
3. Kawski M. Syst. Control. Lett., 1989, 12: 169–175. https://doi.org/10.1016/0167-6911(89)90010-8
4. Cheng D., Lin W. IEEE Trans. Autom. Control., 2003, 48: 1242–1248. https://doi.org/10.1109/TAC.2003.814270
5. Hong Y., Wang J. Sci. China. Ser. F, 2006, 49, No. 1: 80–89. https://doi.org/10.1007/s11432-004-5114-1
6. Long L., Zhao J. Int. J. Contr., 2011, 84, No. 10: 1612–1626. https://doi.org/10.1080/00207179.2011.622790
7. Liao D. J. Theor. and Appl. Inform. Technol., 2012, 46, No. 1: 371–376.
8. Gao F., Li P., Yuan F. J. Inform. and Comput. Sci., 2013, 10, No. 4: 1139–1147. https://doi.org/10.12733/jics20101443
