Symbolic analysis of switching systems: Application to bifurcation analysis of DC/DC switching converters

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 52, Issue 8, 2005, Pages 1632-1643

  Dai, Dong ^a   Tse, Chi K ^a   Ma, Xikui ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Bifurcation; Border collision; Nonsmooth system; Switching converter; Symbolic analysis; Symbolic sequence

Indexed keywords

BIFURCATION (MATHEMATICS); ELECTRIC NETWORK TOPOLOGY; SWITCHING CIRCUITS; SWITCHING SYSTEMS; VOLTAGE CONTROL;

BIFURCATION ANALYSIS; BORDER COLLISION; NONSMOOTH SYSTEM; SWITCHING CONVERTER; SYMBOLIC ANALYSIS; SYMBOLIC SEQUENCE;

POWER CONVERTERS;

EID: 26444535698     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2005.852029     Document Type: Article

References (17)

1. S. Banerjee and G. Vergbese, Eds., Nonlinear Phenomena in Power Electronics. New York: IEEE Press, 2000.
2. C. K. Tse and M. di Bernardo, "Complex behavior of switching power converters," Proc. IEEE, vol. 90, no. 5, pp. 768-781, May 2002.
3. C. K. Tse, Complex Behavior of Switching Power Converters. Boca Raton, FL: CRC, 2003.
4. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos. Chichester, U.K.: Wiley, 2000.
5. M. di Bernardo, M. I. Feigin, and S. J. Hogan, "Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical system," Chaos. Solitions Fractals, vol. 10, no. 11, pp. 1881-1908, 1999.
6. H. E. Nusse and J. A. Yorke, "Border-collision bifurcations including 'period two to period three' for piecewise-smooth systems," Physica D. vol. 57, no. 1, pp. 39-57, Jun. 1992.
7. H. E. Nusse, E. Ott, and J. A. Yorke, "Border-collision bifurcations: an explanation for observed bifurcation phenomena," Phys. Rev. E, vol. 49, no. 2, pp. 1073-1078, Feb. 1994.
8. H. E. Nusse and J. A. Yorke, "Border-collision bifurcations for piece-wise-smooth one-dimensional maps," Int. J. Bifur. Chaos, vol. 5, no. 1, pp. 189-207, Jan. 1995.
9. S. Banerjee, P. Ranjan, and C. Grebogi, "Bifurcations in two-dimensional piecewise-smooth maps - Theory and application s in switching circuits," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 5, pp. 633-643, May 2000.
10. S. Banerjee, E. Ott, J. A. Yorke, and G. H. Yuan, "Anomalous bifurcations in dc-dc converters: borderline collisions in piecewise-smooth maps," in IEEE Power Electron. Specialists Conf., 1997, pp. 1337-1344.
11. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. Boca Raton, FL: CRC, 1999.
12. E. Fossas and G. Olivar, "Study of chaos in the buck converter," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, no. 1, pp. 13-25, Jan. 1996.
13. Y. Ma, H. Kawakami, and C. K. Tse, "Analysis of bifurcation in switched dynamical systems with periodically moving borders," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 51, no. 6, pp. 1184-1193, Jun. 2004.
14. M. di Bernardo and F. Vasca, "Discrete-time maps for the analysis of bifurcations and chaos in dc/dc converters," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 2, pp. 130-143, Feb. 2000.
15. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag, 1989.
16. B.-L. Hao and W. M. Zheng, Applied Symbolic Dynamics and Chaos, Singapore: World Scientific, 1998.
17. G. Olivar, E. Fossas, and C. Batlle, "Bifurcation and chaos in converters: discontinuous vector fields and singular Poincaré maps," Nonlinearity, vol. 13, no. 4, pp. 1095-1121, Jul. 2000.