Synchronization in arrays of coupled nonlinear systems: Passivity circle criterion and observer design

ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings

Volumn 3, Issue , 2001, Pages 692-695

  Wu, Chai Wah ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCLE CRITERION; COUPLED ARRAYS; COUPLED NONLINEAR SYSTEMS; LIPSCHITZ NONLINEAR SYSTEMS; OBSERVER DESIGN; STABILITY CONDITION;

STABILITY CRITERIA; SYNCHRONIZATION; ASYMPTOTIC STABILITY; CONTROL THEORY; LYAPUNOV METHODS; MATRIX ALGEBRA;

NONLINEAR SYSTEMS;

COUPLED ARRAYS;

EID: 0035005407     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISCAS.2001.921405     Document Type: Conference Paper

References (17)

1. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems", Physical Review Letters, vol. 64, pp. 821-824, Feb. 1990.
2. L. M. Pecora and T. L. Carroll, "Driving systems with chaotic signals", Physical Review A, vol. 44, pp. 2374-2383, Aug. 1991.
3. R. He and P. G. Vaidya, "Analysis and synthesis of synchronous periodic and chaotic systems", Physical Review A, vol. 46, pp. 7387-7392, Dec. 1992.
4. C. W. Wu and L. O. Chua, "A unified framework for synchronization and control of dynamical systems", International Journal of Bifurcation and Chaos, vol. 4, no. 4, pp. 979-998, 1994.
5. P. F. Curran, J. A. K. Suykens, and L. O. Chua, "Absolute stability theory and master-slave synchronization", International Journal of Bifurcation and Chaos, vol. 7, no. 12, pp. 2891-2896. 1997.
6. H. Nijmeijer and I. M. Y. Mareels, "An observer looks at synchronization", IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 882-890, 1997. (Pubitemid 127768190)
7. G. Grassi and S. Mascolo, "Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal", IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 1011-1014, 1997. (Pubitemid 127768204)
8. C. W. Wu, "Synchronization in arrays of coupled chaotic circuits and systems: Theory and applications." in Controlling Chaos and Bifurcations in Engineering Systems (G. Chen, ed.), ch. 23, Boca Raton, FL: CRC Press, 1999.
9. L. O. Chua and D. N. Green, "A qualitative analysis of the behavior of dynamic nonlinear networks: Steady-state solutions of nonautonomous networks", IEEE Transactions on Circuits and Systems, vol. 23, pp. 530-550. Sept. 1976.
10. T. Yoshizawa, Stability Theory by Liapunov's Second Method. The mathematical society of Japan, 1966.
11. C. W. Wu and L. O. Chua, "Synchronization in an array of linearly coupled dynamical systems", IEEE Transactions on Circuits and Systems-I: Fundamental Theorv and Applications, vol. 42, pp. 430-447, Aug. 1995.
12. C. W. Wu and L. O. Chua, "Application of Kronecker products to the analysis of systems with uniform linear coupling", IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 42, pp. 775-778, Oct. 1995.
13. L. O. Chua and D. N. Green, "A qualitative analysis of the behavior of dynamic nonlinear networks: Stability of autonomous networks", IEEE Transactions on Circuits and Systems, vol. 23, pp. 355-379, June 1976.
14. M. Vidyasagar, Nonlinear Systems Analysis. New Jersey: Prentice-Hall, 2nd ed., 1993.
15. R. Rajamani, "Observers for Lipschitz nonlinear systems", IEEE Transactions on Automatic Control, vol. 43, pp. 397-401, Mar. 1998. (Pubitemid 128737358)
16. K. S. Fink, G. Johnson, T. Carroll, D. Mar, and L. Pecora, "Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays", Physical Review E, vol. 61, pp. 5080-5090, May 2000.
17. C. W. Wu and L. O. Chua, "Application of graph theory to the synchronization in an array of coupled nonlinear oscillators", IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 42, pp. 494-497, Aug. 1995.