Title :
On the stability and vibrational stabilization of a class of nonlinear systems
Author :
Aleksandrov, Alexander Yu ; Platonov, Alexey V.
Author_Institution :
Dept. of Appl. Math., St. Petersburg State Univ., Russia
Abstract :
A certain class of nonlinear oscillatory systems is investigated. The method of construction of Lyapunov´s functions is suggested to obtain sufficient conditions of asymptotic stability and instability of the equilibrium position for systems considered. The influence of the nonautonomous perturbations on the asymptotic behavior of solutions is studied. The conditions under which the equilibrium position may be stabilized by means of the periodic variations of system parameters are investigated.
Keywords :
Lyapunov methods; asymptotic stability; nonlinear control systems; perturbation techniques; vibration control; Lyapunov functions; asymptotic stability; instability; nonautonomous perturbations; nonlinear oscillatory systems; sufficient conditions; vibrational stabilization; Asymptotic stability; Equations; Linear matrix inequalities; Lyapunov method; Mathematics; Milling machines; Nonlinear systems; Sufficient conditions;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1236858
