Stabilizing with a hammer

Stochastics and Dynamics

Volumn 8, Issue 1, 2008, Pages 47-57

  Sanz Serna, J M ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Random impulses; Stochastic stabilization

Indexed keywords

EID: 44049087242     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493708002263     Document Type: Article

References (13)

1. L. Arnold, H. Crauel and V. Wihstutz, Stabilization of linear systems by noise, SIAM J. Control Optim. 21 (1983) 451-461.
2. L. Arnold, Stabilization by noise revisited, Z. Angew. Math. Mech. 70 (1990) 235-246.
3. F. Colonius and W. Kliemann, The Dynamics of Control (Birkhäuser, 2000).
4. H. Crauel, T. Damm and A. Ilchmann, Stabilization of linear systems by rotation, J. Diff. Eqns. 234 (2007) 412-438.
5. E. Faou and T. Lelièvre, Conservative stochastic differential equations: Mathematical and numerical analysis, preprint.
6. L. Grüne, Asymptotic controllability and exponential stabilization of nonlinear control systems at singular point, SIAM J. Control Optim. 36 (1998) 1585-1603.
7. P. Imkeller and Ch. Lederer, Some formulas for Lyapunov exponents and rotation numbers in two dimensions and the stability of the harmonic oscillator and the inverted pendulum, Dyn. Syst. 16 (2001) 29-61.
8. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, 1992).
9. M. Levi, Geometry and physics of averaging with applications, Physica D 132 (1999) 150-164.
10. G. J. Mata and E. Pestana, Effective Hamiltonian and dynamic stability of the inverted pendulum, Eur. J. Phys. 25 (2004) 717-721.
11. R. Mitchell, Stability of the inverted pendulum subjected to almost periodic and stochastic base motion - an application of the method of averaging, Int. J. Nonlinear Mech. 7 (1972) 101-123.
12. A. I. Ovseyevich, The stability of an inverted pendulum when there are rapid random oscillations of the suspension point, J. Appl. Math. Mech. 70 (2006) 762-768.
13. J. M. Sanz-Serna and A. M. Stuart, Ergodicity of dissipative differential equations subject to random impulses, J. Diff. Eqns. 155 (1999) 262-284.