Stability analysis of quasi-polynomial dynamical systems with applications to biological network models

Automatica

Volumn 48, Issue 11, 2012, Pages 2945-2950

  Motee, Nader ^a   Bamieh, Bassam ^b   Khammash, Mustafa ^c  

^a Lehigh University   (United States)

^b University of California   (United States)

^c SWISS FEDERAL INSTITUTE OF TECHNOLOGY   (Switzerland)

Author keywords

Asymptotic stability; Complex systems; Interconnected systems; Nonlinear systems; Stability analysis

Indexed keywords

BIOCHEMICAL NETWORK; BIOLOGICAL NETWORKS; CANONICAL FORM; GENERALIZED MASS; HIGHER-DIMENSIONAL; INITIAL CONDITIONS; LOTKA-VOLTERRA; ORTHANT; PARAMETERIZED MODEL; QUASI-POLY-NOMIAL; REDUCED ORDER MODELS; SPECIAL CLASS; STABILITY ANALYSIS; SYSTEM APPLICATIONS;

ALGEBRA; ASYMPTOTIC STABILITY; DYNAMICAL SYSTEMS; EMBEDDED SYSTEMS; LARGE SCALE SYSTEMS; NONLINEAR SYSTEMS; POLYNOMIAL APPROXIMATION;

BIOLOGICAL SYSTEMS;

EID: 84867401723     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2012.06.094     Document Type: Article

References (18)

1. M. Arcak, and E. Sontag Diagonal stability of a class of cyclic systems and its connection with the secant criterion Automatica 42 9 2006 1531 1537
2. M. Arcak, and E. Sontag A passivity-based stability criterion for a class of biochemical reaction networks Mathematical Biosciences and Engineering 5 1 2008 1 19
3. Chandra, F.A.; Buzi, G.; & Doyle, J.C. (2009). Linear control analysis of the autocatalytic glycolysis system. In Proceedings of the American control conference.
4. E. Feron, S. Boyd, L. El Ghaoui, and V. Balakrishnan Linear matrix inequalities in system and control theory 1997 Society for Industrial Mathematics
5. A. Figueiredo, I.M. Gléria, and T.M. Rocha Filho Boundedness of solutions and Lyapunov functions in quasi-polynomial systems Physics Letters A 268 2000 335 341
6. R. Ghaemi, J. Sun, P. Iglesias, and D. Del Vecchio A method for determining the robustness of bio-molecular oscillator models BMC Systems Biology 3 2009 95
7. B.S. Goh Global stability in many-species systems The American Naturalist 111 977 1977 135 143
8. B. Hernandez-Bermejo Stability conditions and Liapunov functions for quasi-polynomial systems Applied Mathematics Letters 15 1 2002 25 28
9. B. Hernandez-Bermejoa, and V. Fairen Lotka-Volterra representation of general nonlinear systems Mathematical Biosciences 140 1 1997 1 32
10. R.A. Horn, and C.R. Johnson Matrix analysis 1990 Cambridge University Press
11. D.H. Irving, E.O. Voit, and M.A. Savageau Analysis of complex dynamic networks with ESSYNS E.O. Voit, Canonical non-linear modelling S-systems approach to understanding complexity 1991 Von Nostrand Reinhold
12. M.R. Jovanović, M. Arcak, and E.D. Sontag A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure IEEE Transactions on Automatic Control: Special Issue on Systems Biology 53 2008 75 86
13. E. Kaszkurewicz, and A. Bhaya Matrix diagonal stability in systems and computation 2000 Birkhauser Boston
14. H. Kitano Towards a theory of biological robustness Molecular Systems Biology 3 2007 137
15. M.T. Laub, and W.F. Loomis A molecular network that produces spontaneous oscillations in excitable cells of dictyostelium Molecular Biology of the Cell 9 1998 3521 3532
16. Magyar, A.; Szederknyi, G.; & Hangos, K.M. (2005). Quasi-polynomial system representation for the analysis and control of nonlinear systems. In 16th IFAC world congress. Prague, Czech Republic.
17. L. Ma, and P.A. Iglesias Quantifying robustness of biochemical network models BMC Bioinformatics 3 38 2002 38 50
18. G. Poole, and T. Boullion A survey on m-matrices SIAM Review 16 4 1974 419 427