Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.3175.3182Gholizade-NarmH.AzemiA.KhademiM.Karimi-GhartemaniM.122008818In this study a synchronization method is developed
to prevent the blocking arrhythmias which are caused by lack of synchronization
between the two major heart pacemakers called the Sino-Atrial (SA) node
and Atrio-Ventricullar (AV) node. Such pacemakers can be modeled by the
Van der Pol oscillators. Feedback linearization method is used in synchronization.
Since all states are not always available, they are estimated by a new
observer in this research. To design the observer, first we introduce
a robust observer for a unique Van der Pol oscillator. The robustness
of proposed observer is obtained using gain and phase margins test. The
observer variables are such that the error dynamical system is linear
time varying and we use describing function method to prove its convergence.
This observer is then extended to two unidirectional and bidirectional
coupled Van der Pol Oscillators. To prove the stability, a novel nonlinear
function structure is introduced to seclude the coupled Van der Pol oscillators
to two isolated oscillators. The performance of the proposed method is
investigated by numerical simulations.]]>Brando, D.D., M.G. Signorini and S. Cerutti, 1998Fitzhugh, R.,1961Floret-Ponet, F. and F. Lamnabhi-Lagarrigue, 2001Grudzinsky, K. and J. Zebrowski,2004Guyton, A.C. and J.E. Hall,2005Hua, C., X. Guan, X. Li and P. Shi, 2004Julier, S.J. and J.K. Uhlmann,1997Kalman, R.E., 1960Liao, T.L. and N.S. Huang,1999Nagumo, J., S. Arimoto and S. Yoshizawa,1962Pearson, J.D., 1962Sato, S., S. Doi and T. Nomura,1994Slotine, J.E. and W. Li,1991Van Der Pol, B. and J. Van Der Mark,1927Zhang, C., X.X. Zhou, Y.J. Cao and Q.H. Wu,1999