Geometric Properties of Dynamic Nonlinear Networks: Transversality, Local-Solvability and Eventual Passivity

IEEE Transactions on Circuits and Systems

Volumn 28, Issue 5, 1981, Pages 406-428

  Ichiraku, Sheigo ^c   Chua, Leon O ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TOKUSHIMA   (Japan)

^c YOKOHAMA CITY UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC NETWORKS, NONLINEAR;

EID: 0019570820     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1981.1085003     Document Type: Article

References (14)

1. L. O. Chua and D. N. Green, “Graph theoretic properties of dynamic nonlinear networks,” IEEE Trans. Circuits Syst., vol. CAS-23, pp. 293–311, May 1976
2. A. L. Sangiovanni-Vincentelli and Y. T. Wang, “On equivalent dynamic networks: Elimination of capacitor-loops and inductor-cut sets,” IEEE Trans. Circuits Syst., vol. CAS-25, pp. 174–177, Mar. 1978
3. L. O. Chua, T. Matsumoto, and S. Ichiraku, “Geometric properties of resistive nonlinear n-ports: Transversality, structural stability, reciprocity, and anti-reciprocity,” IEEE Trans. Circuits Syst., vol. CAS-27, 577–603, July 1980
4. T. Matsumoto, “On several geometric aspects of nonlinear networks,” works,” J. Franklin Inst., vol. 301, nos. 1 and 2, pp. 203–225, 1976
5. C. A. Desoer and F. F. Wu, “Trajectories of RLC networks: Geometric approach,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 562–570, Dec. 1972
6. M. W. Hirsch, Differential Topology. New York: Springer-Verlag, 1976
7. L. O. Chua and N. N. Wang, “Complete stability of autonomous reciprocal nonlinear networks,” Int. J. Circuit Theory Appl., vol. 6, pp. 211–271, 1978
8. S. Smale, “On the mathematical foundations of electrical circuit theory,” J. Differential Geometry, vol. 17, pp. 193–210, 1972
9. T. Roska, “On the uniqueness of solutions of nonlinear dynamic networks,” IEEE Trans. Circuits Syst., vol. CAS-25, pp. 161–168, 1978
10. T. Matsumoto, “On the dynamics of electrical networks,” J. Differential Equations, vol. 21, pp. 179–196, May 1976
11. I. C. Göcknar, “On the state description of nonlinear networks,” Proc. IEEE, vol. 68, pp. 734–735, June 1980
12. L. O. Chua and D. N. Green, “A qualitative analysis of the behavior of dynamic nonlinear networks: Stability of autonomous networks,” IEEE Trans. Circuits Syst., vol. CAS-23, pp. 355–379, June 1976
13. L. O. Chua and D. N. Green, “A qualitative analysis of the behavior of dynamic nonlinear networks: Steady-state solutions of non-autonomous networks,” IEEE Trans. Circuits Syst., vol. CAS-23, 23, pp. 530–550, Oct. 1976
14. T. Matsumoto, “Eventually passive nonlinear networks,” IEEE Trans. Circuits Syst., vol. CAS-24, pp. 261–269, May 1977