On the stability domain estimation via a quadratic Lyapunov function: Convexity and optimality properties for polynomial systems

IEEE Transactions on Automatic Control

Volumn 41, Issue 11, 1996, Pages 1650-1657

  Tesi, A ^a   Villoresi, F ^a   Genesio, R ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; LYAPUNOV METHODS; OPTIMIZATION; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING; SYSTEM STABILITY;

CONVEX OPTIMIZATION PROBLEM; STABILITY DOMAIN ESTIMATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0030287556     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.544002     Document Type: Article

References (20)

1. H. K. Khalil, Nonlinear Systems. New York: McMillan, 1992.
2. R. Genesio, M. Tartaglia, and A. Vicino, "On the estimation of asymptotic stability region - State of the art and new proposals," IEEE Trans. Automat. Contr., vol. AC-30, pp. 747-755, 1985.
3. E. J. Davison and E. M. Kurak, "A computational method for determining quadratic Lyapunov functions for nonlinear systems," Automation, vol. 7, pp. 627-636, 1971.
4. A. N. Michel, N. R. Sarabudla, and R. K. Miller, "Stability analysis of complex dynamical systems - Some computational methods," Circ. Syst. Signal Processing, vol. 1, pp. 561-573, 1982.
5. H. D. Chiang and J. S. Thorp, "Stability regions of nonlinear dynamical systems: A constructive methodology," IEEE Trans. Automat. Contr., vol. 34, pp. 1229-1241, 1989
6. J. Hauser and M. C. Lai, "Estimating quadratic stability domains by nonsmooth optimization," 1992 Amer. Contr. Conf., Chicago, IL, pp. 571-576.
7. M. C. Lai and J. Hauser, "Computing maximal stability region using a given Lyapunov function," 1993 Amer. Contr. Conf., San Franciso, CA, pp. 1500-1502.
8. R. Habermann, Mathemathical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow. Englewood Cliffs, NJ: Prentice-Hall, 1977.
9. E. Beltrami, Mathematics for Dynamic Modeling. Boston: Academic, 1987.
10. D. E. Koditschek and K. S. Narendra, "The stability of second-order quadratic differential equations," IEEE Trans. Automat. Contr., vol. AC-27, pp. 783-798, 1982.
11. R. Genesio and A. Vicino, "Some results on the asymptotic stability of second-order nonlinear systems," IEEE Trans. Automat. Contr., vol. AC-29, pp. 857-861, 1984.
12. R. Genesio and A. Tesi, "Stability analysis of quadratic systems," Preprints IFAC Symp. NOLCOS 89, Capri, pp. 226-230.
13. R. Genesio, A. Tesi, and F. Villoresi, "A structural approach for computing stability domains of polynomial systems," in Proc. 1993 IEEE Int. Conf. Syst., Man Cybernetics, pp. 80-85, Le Touquct, France, 1993.
14. W. Hahn, Stability of Motion. Berlin: Springer-Verlag, 1967.
15. W. J. Rugh, Nonlinear System Theory - The Volterra/Wiener Approach. Baltimore: Johns Hopkins Univ. Press, 1981.
16. A. Graham, Kronecker Products and Matrix Calculus with Applications. Chichester: Ellis Horwood, 1981.
17. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore: John Hopkins Univ. Press, 1989.
18. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia: Siam, 1994.
19. Yu. Nesterov and A. Nemirovsky, Interior Point Polynomial Methods in Convex Programming: Theory and Applications. Philadelphia: Siam, 1993.
20. J. H. Fu and E. H. Abed, "Families of Lyapunov functions for nonlinear systems in critical cases," IEEE Trans. Automat. Contr., vol. 38, pp. 3-16, 1993.