Improved condition for stabilization of controlled invertedpendulum under stochastic perturbations
作者： Leonid Shaikhet ,
DOI: 10.3934/DCDS.2009.24.1335
关键词: Lyapunov functional 、 General method 、 Control theory 、 Physics 、 Double inverted pendulum 、 Double pendulum 、 Inverted pendulum 、 Stability conditions
摘要: Known sufficient condition for stabilization of the controlled inverted pendulum under stochastic perturbations is improved via V.Kolmanovskii and L.Shaikhet general method Lyapunov functionals construction.
sci-hub.st 参考文章(12)
Richard Sharp, Yen-Hsi Tsai, Björn Engquist, Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem Springer, Berlin, Heidelberg. pp. 241- 261 ,(2005) , 10.1007/3-540-26444-2_13
Mark Levi, Stability of the Inverted Pendulum—A Topological Explanation SIAM Review. ,vol. 30, pp. 639- 644 ,(1988) , 10.1137/1030140
J. M. SANZ-SERNA, STABILIZING WITH A HAMMER Stochastics and Dynamics. ,vol. 08, pp. 47- 57 ,(2008) , 10.1142/S0219493708002263
Nataliya Bradul, Leonid Shaikhet, None, Stability of the Positive Point of Equilibrium of Nicholson's Blowflies Equation with Stochastic Perturbations: Numerical Analysis Discrete Dynamics in Nature and Society. ,vol. 2007, pp. 1- 25 ,(2007) , 10.1155/2007/92959
R. Mitchell, Stability of the inverted pendulum subjected to almost periodic and stochastic base motion—An application of the method of averaging International Journal of Non-Linear Mechanics. ,vol. 7, pp. 101- 123 ,(1972) , 10.1016/0020-7462(72)90025-X
A.I. Ovseyevich, The stability of an inverted pendulum when there are rapid random oscillations of the suspension point Journal of Applied Mathematics and Mechanics. ,vol. 70, pp. 762- 768 ,(2006) , 10.1016/J.JAPPMATHMECH.2006.11.010
Gustavo J Mata, E Pestana, Effective Hamiltonian and dynamic stability of the inverted pendulum European Journal of Physics. ,vol. 25, pp. 717- 721 ,(2004) , 10.1088/0143-0807/25/6/003
Peter Imkeller, Christian Lederer, Some formulas for Lyapunov exponents and rotation numbers in two dimensions and the stability of the harmonic oscillator and the inverted pendulum Dynamical Systems-an International Journal. ,vol. 16, pp. 29- 61 ,(2001) , 10.1080/02681110010001289
D. J. Acheson, T. Mullin, Upside-down pendulums Nature. ,vol. 366, pp. 215- 216 ,(1993) , 10.1038/366215B0
James A. Blackburn, H. J. T. Smith, N. Gro/nbech‐Jensen, Stability and Hopf bifurcations in an inverted pendulum American Journal of Physics. ,vol. 60, pp. 903- 908 ,(1992) , 10.1119/1.17011