On the expansion schemes in trajectory reversing method


  • Ştefan Măruşter University of the West, Timisoara, Romania




nonlinear dynamical systems, stability regions, trajectory reversing method, expansion schemes
Abstract views: 167


The paper deals with certain expansion schemes in trajectory reversing method for estimating asymptotic stability region of nonlinear dynamical systems. The asymptotic behavior of the sequence of estimates is investigated. Some numerical examples are given.


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Bogacki, P., Weistein, S. and Xu, Y., Distances between oriented curves in geometric modeling, Adv. Comp. Math., 7, pp. 593-621, 1997, https://doi.org/10.1023/A:1018923609019 DOI: https://doi.org/10.1023/A:1018923609019

Chiang, H., Hirsch, M.W. and Wu, F.F., Stability regions of nonlinear autonomous systems, IEEE Trans. Aut. Control, 33, pp. 16-27, 1988, https://doi.org/10.1109/9.357 DOI: https://doi.org/10.1109/9.357

Chiang, H. and Thorp, J. S., Stability regions of nonlinear dynamical systems: a costructive methodology, IEEE Trans. Aut. Control, 34, pp. 1229-1241, 1989, https://doi.org/10.1109/9.40768 DOI: https://doi.org/10.1109/9.40768

Genesio, R., Tartaglia, M., and Vicino, A., On the estimation of asymptotic stability regions: state of the art and new proposals, IEEE, Trans. on Aut. Control, AC-30, no. 8, pp. 747-755, 1985, https://doi.org/10.1109/TAC.1985.1104057 DOI: https://doi.org/10.1109/TAC.1985.1104057

Genesio, R. and Vicino, A., New techniques for constructing asimptotic stability regions for nonlinear systems, IEEE Trans. Circuits Syst., CAS-31, pp. 574-581, 1984, https://doi.org/10.1109/TCS.1984.1085537 DOI: https://doi.org/10.1109/TCS.1984.1085537

Guttalu, R. and Flashner, H., A numerical method for computing domains of attraction for dynamical systems, Intern. J. Numer. Meth. Engrg., 26, pp. 875-890, 1988, https://doi.org/10.1002/nme.1620260409 DOI: https://doi.org/10.1002/nme.1620260409

Hahn, W., Theory and Applications of Lyapunov's Direct Method, Prentice Hall, Englewood Cliffs, NJ, 1963.

Hsu, C. S., Yee and Cheng, H. C., Determination of global regions of asymptotic stability for difference dynamical systems, J. Appl. Mech., 44, pp. 147-153, 1977, https://doi.org/10.1115/1.3423981 DOI: https://doi.org/10.1115/1.3423981

Loccufier, M. and Noldus, E., A new trajectory reversing method for estimating stability regions of autonomous nonlinear systems, Nonlinear Dynamics, 21, pp. 265-288, 2000, https://doi.org/10.1023/A:1008311427709 DOI: https://doi.org/10.1023/A:1008311427709

Maruşter, Şt., Experiments on the regions of asymptotic stability, An. Univ. Timisoara, ser. Sti. Math., XXVI, fasc. 3, pp. 53-66, 1988.

Michel, A. N., Sarabudla, N. R. and Miller, R. K., Stability analysis of complex dynamical systems some computational methods, Cir. Syst. Sign. Process, 1, pp. 171-202, 1982. DOI: https://doi.org/10.1007/BF01600051

Ortega, J. M. and Rheinboldt, W.C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

Rus, I., Principles of the Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1980 (in Romanian).

Stacey, A. J. and Stonier, R. J., Analitic estimatesfor the boundary of the region of asymptotic attraction, Dynam. Control, 8, no. 2, pp. 177-189, 1998, https://doi.org/10.1023/A:1008223530175 DOI: https://doi.org/10.1023/A:1008223530175




How to Cite

Măruşter, Ştefan. (2002). On the expansion schemes in trajectory reversing method. Rev. Anal. Numér. Théor. Approx., 31(1), 89–101. https://doi.org/10.33993/jnaat311-711