Diagonal stability on cactus graphs

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 6553-6558

  Arcak, Murat ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY;

BIOCHEMICAL REACTION NETWORK; BIOLOGICAL NETWORKS; DIAGONAL MATRICES; INTERCONNECTION STRUCTURE; PASSIVITY PROPERTIES; SECANT CRITERION; SIMPLE CIRCUITS; STABILITY OF INTER-CONNECTED SYSTEMS;

STABILITY;

EID: 79953134377     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717799     Document Type: Conference Paper

References (11)

1. V. Volterra, Lȩcons sur la théorie mathématqiue de la lutte pour la vie. Paris: Gauthier-Villars, 1931.
2. R. Redheffer, "Volterra multipliers - Parts I and II," SIAM Journal on Algebraic and Discrete Methods, vol. 6, no. 4, pp. 592-623, 1985.
3. E. Kaszkurewicz and A. Bhaya, Matrix Diagonal Stability in Systems and Computation. Boston: Birkhauser, 2000.
4. G. Cross, "Three types of matrix stability," Linear Algebra and its Applications, vol. 20, pp. 253-263, 1978.
5. A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Philadelphia: Society for Industrial and Applied Mathematics, Classics in Applied Mathematics, 1994, (Originally published by Academic Press, New York, 1979.).
6. J. Wen and M. Arcak, "A unifying passivity framework for network flow control," IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 162-174, 2004.
7. M. Arcak and E. Sontag, "Diagonal stability of a class of cyclic systems and its connection with the secant criterion," Automatica, vol. 42, no. 9, pp. 1531-1537, 2006.
8. -, "A passivity-based stability criterion for a class of biochemical reaction networks," Mathematical Biosciences and Engineering, vol. 5, no. 1, pp. 1-19, 2008.
9. C. Berge, The Theory of Graphs. Mineola, New York: Dover Publications, Inc., 2001, (Originally published: The theory of graphs and its applications. Wiley, 1962.).
10. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, ser. SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1994, vol. 15.
11. M. Bona, M. Bousquet, G. Labelle, and P. Leroux, "Enumeration of m-ary cacti," Advances in Applied Mathematics, vol. 24, pp. 22-56, 2000.