Input and output coupled nonlinear systems

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 52, Issue 3, 2005, Pages 567-575

  Duan, Zhisheng ^a   Wang, Jin Zhi ^a   Huang, Lin ^a  

^a Peking University   (China)

Author keywords

Coupled Chua's circuit; Global convergence; Input and output interconnection; Input transformation; Nonlinear systems with multiple equilibria

Indexed keywords

ASYMPTOTIC STABILITY; CHAOS THEORY; CONTROL THEORY; CONVERGENCE OF NUMERICAL METHODS; FREQUENCY DOMAIN ANALYSIS; LARGE SCALE SYSTEMS; MATRIX ALGEBRA;

COUPLED CHUA CIRCUIT; GLOBAL CONVERGENCE; INPUT TRANSFORMATION; INPUT-AND-OUTPUT INTERCONNECTION; NONLINEAR SYSTEMS-WITH-MULTIPLE EQUILIBRIA;

NONLINEAR CONTROL SYSTEMS;

EID: 11144257657     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2004.842873     Document Type: Article

References (26)

1. G. A. Leonov, D. V. Ponomarenko, and V. B. Smirnova, Frequency-Domain Method for Nonlinear Analysis: Theory and Applications. Singapore: World Scientific, 1996.
2. G. A. Leonov, I. M. Burkin, and A. L. Shepeljavyi, Frequency Methods in Oscillation Theory. Dordrecht, The Netherlands: Kluwer, 1992.
3. J. L. Moiola and G. R. Chen, Hopf Bifurcation Analysis: A Frequency-Domain Method. Singapore: World Scientific, 1996.
4. M. Basso, R. Genesio, and A. Tesi, "Frequency domain methods and control of complex dynamics," in Proc. 37th IEEE Circuits Devices Conf., Tampa, FL, 1996.
5. U. Jonson, C. Y. Kao, and A. Megretski, "Robustness of periodic trajectories," IEEE Trans. Autom. Control, vol. 47, no. 11, pp. 1842-1856, Nov. 2002.
6. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, Singapore: World Scientific, 1998.
7. T. Imai, K. Konishi, H. Kokame, and K. Hirata, "An experimental suppression of spatial instability in one-way open coupled Chua's circuits," Int. J. Bifurc. Chaos, vol. 12, pp. 2897-2905, 2002.
8. T. Kapitaniak, L. O. Chua, and G. Q. Zhong, "Experimental hyperchaos in coupled Chua's circuits," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 41, no. 5, pp. 499-503, May 1994.
9. R. Madan, Chua's Circuit: A Paradigm for Chaos, Singapore: World Scientific, 1993.
10. J. A. K. Suykens, P. F. Curran, J. Vandewalle, and L. O. Chua, "Robust nonlinear H8∞ synchronization of chaotic Lur'e systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 10, pp. 891-904, Oct. 1997.
11. J. A. K. Suykens, T. Yang, and L. O. Chua, "Impulsive synchronization of chaotic Lur'e systems by measurement feedback," Int. J. Bifurc. Chaos, vol. 8, no. 6, pp. 1371-1381, 1998
12. D. D. Siljak, Large-Scale Dynamic Systems. New York: North-Holland, 1978.
13. Z. S. Duan, L. Huang, L. Wang, and J. Z. Wang, "Some applications of small gain theorem to interconnected systems," Syst. Contr. Lett. vol. 52, no. 3-4, pp. 263-273, 2004.
14. Z. S. Duan, J. Z. Wang, and L. Huang, "Multi-input and multi-output nonlinear systems: Interconnected Chua's circuits," Int. J. Bifurc. Chaos, vol. 14, no. 9, pp. 3065-3081, 2004.
15. R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control: Theory and Applications. London, U.K.: Springer-Verlag, 2000.
16. A. Rantzer, "On the Kalman-Yakubovich-Popov lemma," Syst. Contr. Lett., vol. 28, pp. 7-10, 1996.
17. W. Sun, P. P. Khargonekar, and P. P. Shim, "Solution to positive real control problem for linear time-invariant systems," IEEE Trans. Autom. Contr.., vol. 39, no. 10, pp. 2034-2046, Oct. 1994.
18. A. Helmersson, Methods for Robust Gain Scheduling. Linkoping, Sweden: Linkoping Univ., 1995.
19. T. Iwasaki and R. E. Skelton, "All controllers for the general H∞ control problem: LMI existence conditions and state space formulas," Automatica, vol. 30, pp. 1307-1317, 1994.
20. R. E. Kalman, "Physical and mathematical mechanisms of instability in nonlinear automatic control systems," Trans. Amer. Soc. Mech. Eng. vol. 79, no. 3, pp. 553-563, 1957.
21. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
22. W. M. Wonham, Linear Multivariable Control: A Geometric Approach. New York: Springer-Verlag, 1979.
23. R.N. Shorten, O. Mason, F. O'cairbre, and P. Curran, "A unifying framework for the SISO circle criterion and other quadratic stability criteria," Int. J. Contr., vol. 77, no. 1, pp. 1-8, 2004.
24. R. N. Shorten and K. S. Narendra, "On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form," IEEE Trans. Autom. Contr., vol. 48, no. 4, pp. 618-621, Apr. 2003.
25. M. Yalcin, J. A. K. Suykens, J. Vandewalle, and S. Ozoguz, "Families of scroll grid attractors," Int. J. Bifurc. Chaos, vol. 12, no. 1, pp. 23-41, 2002.
26. L. O. Chua, CNN: A Paradigm for Complexity, ser. A. Singapore: World Scientific, 1998, vol. 31.