Analysis of nonlinear time-delay systems using the sum of squares decomposition

Proceedings of the American Control Conference

Volumn 5, Issue , 2004, Pages 4153-4158

  Papachristodoulou, Antonis ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; FREQUENCY DOMAIN ANALYSIS; LYAPUNOV METHODS; MAPPING; MATRIX ALGEBRA; SYSTEM STABILITY;

FUNCTIONAL DIFFERENTIAL EQUATIONS (FDE); LINEAR MATRIX INEQUALITIES (LMI); SEMIDEFINITE PROGRAMMING;

NONLINEAR SYSTEMS;

EID: 8744315412     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/acc.2004.1383959     Document Type: Conference Paper

References (21)

1. P.-A. Bliman. Lyapunov equation for the stability of linear delay systems of retarded and neutral type. IEEE Trans. Automat. Contr., 47(2):327-335, 2002.
2. P.-A. Bliman. Stability of non-linear delay systems: delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method. Int. J. Control, 75(4):265-274, 2002.
3. E.-K. Boukas and Z. Liu. Deterministic and Stochastic Time Delay Systems. Birkhäuser, 2002.
4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), 1994.
5. K. Gu. Discretised LMI set in the stability problem of linear uncertain time-delay systems. International Journal of Control, 68:155-163, 1997.
6. K. Gu, V. L. Kharitonov, and J. Chen. Stability of Time-Delay systems. Birkhäuser, 2003.
7. K. Gu and S.-I. Niculescu. Additional dynamics in transformed time-delay systems. IEEE Trans. Automat. Contr., 36(3):374-384, 2000.
8. J. K. Hale and S. M. V. Lunel. Introduction to Functional Differential Equations. Applied Mathematical Sciences (99). Springer-Verlag, 1993.
9. E. F. Infante and W. V. Castelan. A Lyapunov functional for a matrix difference-differential equation. J. Diff. Equations, 29:439-451, 1978.
10. V. Kolmanovskii and A. Myshkis. Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers, 1999.
11. Y. Kuang. Delay Differential Equations with Applications in Population Dynamics. Academic Press, 1993. Mathematics in Science and Engineering (191).
12. F. Mazenc and S.-I. Niculescu. Lyapunov stability analysis for nonlinear delay systems. Systems and Control Letters, 42:245-251, 2001.
13. J. D. Murray. Mathematical Biology. Springer-Verlag, 1993.
14. S.-I. Niculescu, A. T. Neto, J. M. Dion, and L. Dugard. Delay-dependent stability of linear systems with delayed-state: An LMI approach. In Proc. 35th Conf. Decision and Control, New Orleans, LA, pages 1495-1496, 1995.
15. A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using the sum of squares decomposition. In Proceedings of the 41st IEEE Conf. on Decision and Control, pages 3482-3487, 2002.
16. P. A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, Pasadena, CA, 2000. Available at http://control.ee. ethz.ch/~parrilo/pubs/index.html.
17. S. Prajna, A. Papachristodoulou, and P. Parrilo. Introducing SOSTOOLS: A general purpose sum of squares programming solver. In Proceedings of the 41st IEEE Conf. on Decision and Control, pages 741-746, 2002.
18. S. Prajna, A. Papachristodoulou, and P. A. Parrilo. SOSTOOLS - Sum of Squares Optimization Toolbox, User's Guide. Available at http://www.cds.caltech. edu/sostools and http://www.aut.ee.ethz.ch/~parrilo/sostools, 2002.
19. M. Y. Repin. Quadratic Lyapunov functionals for systems with delay. Prik. Mat. Meh., 29:564-566, 1965.
20. A. R. Teel. Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorems. IEEE Trans. Automat. Contr., 43(7):960-964, 1998.
21. P. J. Wangersky and W. J. Cunningham. Time lag in prey-predator population models. Ecology, 38(1):136-139, 1957.