Periodic orbits arising from Delta-modulated feedback control

Chaos, Solitons and Fractals

Volumn 19, Issue 3, 2004, Pages 581-595

  Xia, Xiaohua ^a   Gai, Rudong ^a,b   Chen, Guanrong ^c  

^a UNIVERSITY OF PRETORIA   (South Africa)

^b LIAONING TECHNICAL UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

DELTA MODULATION; POLYNOMIALS; TIME VARYING SYSTEMS;

PERIODIC ORBITS;

FEEDBACK CONTROL;

EID: 0041629311     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00131-0     Document Type: Article

References (16)

1. Ariyavisitakul S., Chang L. Simulation of a CDMA system performance with feed-back power control. Electron. Lett. 27:1991;2127-2128.
2. Brockett R.W., Leberzon D. Quantized feedback stabilization of linear systems. IEEE Trans. Automat. Control. 45:2000;1279-1289.
3. Delchamps D.F. Stablilizing a linear system with quantized state feedback. IEEE Trans. Automat. Control. 35:1990;916-924.
4. Derrida B., Gervois A., Pomeau Y. Iteration of endomorphisms on the real axis and representation of numbers. Ann. Inst. Henri Poincaré A. XXIX:1978;305-356.
5. Elia N., Mitter S.K. Stabilization of linear systems with limited information. IEEE Trans. Automat. Control. 46:2001;1384-1400.
6. Gai R, Xia X, Chen G. Complex dynamics of systems under delta-modulated control. Technical Report, March 2003. Department of Electrical, Electronic and Computer Engineering, University of Pretoria, South Africa.
7. Heidel J. The existence of periodic orbits of the tent map. Phys. Lett. A. 143:1990;195-201.
8. Hu T., Lin Z., Qiu L. Stabilization of exponentially unstable linear systems with saturating actuators. IEEE Trans. Automat. Control. 46:2001;973-979.
9. Hua L.K., Wang Y. Applications of number theory to numerical analysis. 1981;Springer-Verlag, New York.
10. Imura J., van der Schaft A.J. Characterization of well-posedness of piecewise linear systems. IEEE Trans. Automat. Control. 45:2000;1600-1619.
11. Liberti J.C. Jr., Rappaport T.S. Smart antennas for wireless communications: IS-95 & third generation CDMA applications. 1999;Prentice Hall, New Jersey.
12. Louck J.D., Metropolis N. Symbolic dynamics of trapezoidal maps. 1986;Reidel, Dordrecht.
13. Sarkovskii A.N. Coexistence of cycle of a continuous map of a line into itself. Ukr. Mat. Zh. 16:1964;61-71.
14. Van-der-Schaft A.J., Schumacher J.M. An introduction to hybrid dynamical systems. Lecture notes in control and information sciences. vol. 251:2000;Springer, Berlin.
15. Xia X. Well-posedness of piecewise-linear systems with multiple modes and multiple criteria. IEEE Trans. Automat. Control. 47:2002;1716-1720.
16. Xia X, Chen G. On Delta-modulated control: a simple system with complex dynamics. Technical Report, October 2002. Department of Electrical, Electronic and Computer Engineering, University of Pretoria, South Africa.