TY - JOUR
T1 - Hybrid feedback stabilization of quasilinear systems in the plane
AU - Litsyn, Elena
AU - Nepomnyashchikh, Yurii
AU - Ponosov, Arcady
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected], [email protected] (E. Litsyn), [email protected] (Y. Nepomnyashchikh), [email protected] (A. Ponosov). 1 Partially supported by the Ministry of Science and the Ministry of Absorption, Center for Absorption in Science, Israel. 2 Supported by Tel Aviv University and Ben-Gurion University of the Negev, Israel, by the Research Council of Norway (NFR) and by the RFBR (grants nos. 03-01-00255 and 04-01-96016).
PY - 2005/5/1
Y1 - 2005/5/1
N2 - We apply Artstein's hybrid feedback algorithm to stabilize quasilinear dynamical systems with complex multipliers in the plane. We study only the case of incomplete observation when ordinary feedback controls do not work. The main results of the paper state that Artstein's procedure provides an arbitrary rate of asymptotic convergence/divergence of solutions. In other words, we prove the complete controllability from below of the upper Lyapunov exponent and the uniform upper Lyapunov exponent for the quasilinear systems in question.
AB - We apply Artstein's hybrid feedback algorithm to stabilize quasilinear dynamical systems with complex multipliers in the plane. We study only the case of incomplete observation when ordinary feedback controls do not work. The main results of the paper state that Artstein's procedure provides an arbitrary rate of asymptotic convergence/divergence of solutions. In other words, we prove the complete controllability from below of the upper Lyapunov exponent and the uniform upper Lyapunov exponent for the quasilinear systems in question.
KW - Hybrid feedback control
KW - Quasilinear dynamical systems
KW - Upper Lyapunov exponents
UR - https://www.scopus.com/pages/publications/14844324010
U2 - 10.1016/j.jmaa.2004.12.004
DO - 10.1016/j.jmaa.2004.12.004
M3 - Article
AN - SCOPUS:14844324010
SN - 0022-247X
VL - 305
SP - 347
EP - 366
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -