Polynomial level-set methods for nonlinear dynamical systems analysis

43rd Annual Allerton Conference on Communication, Control and Computing 2005

Volumn 2, Issue , 2005, Pages 640-649

  Wang, Ta Chung ^a   Lall, Sanjay ^a   West, Matthew ^a  

^a Stanford University   (United States)

Author keywords

Domain of attraction; Level set methods; Semi definite programming

Indexed keywords

EID: 84962076535     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. E. J. Davision and E. M. Kurak. A computational method for determining quadratic Lyapunov functions for non-linear systems. Automatica, 7:627-636, 1971.
2. G. Ghesi, A. Tesi, and A. Vicino. On optimal quadratic Lyapunov functions for polynomial systems. In 15th Int. Symp. on Mathematical Theory of Networks and Systems, 2002.
3. Z. W. Jarvis-Wloszek. Lyapunov based analysis and controllers synthesis for polynomial systems using sum-of-squares optimization. PhD thesis, University of California, Berkeley, 2003.
4. H. Khalil. Nonlinear systems. Prentice-Hall Inc., third edition, 2000.
5. S. Lall, M. Peet, and T. Wang. SOSCODE: Sum of squares optimization toolbox for MATLAB, 2005. Available from http://www.stanford.edu/~lall/.
6. J. B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM Journal on Opti-mization, 11(3):796-817, 2001.
7. A. Levin. An analytical method of estimating the domain of attraction for polynomial differential equations. IEEE Transactions on Automatic Control, 39(12):2471-2475, 1994.
8. I. M. Mitchell and C. J. Tomlin. Level set methods for computation in hybrid systems. In Hybrid Systems: Computation and Control, LNCS 1790, pages 310-323. Springer Verlag, 2000.
9. S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer Verlag, 2002.
10. A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using the sum of squares decomposition. In Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
11. P. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimiza-tion. PhD thesis, California Institute of Technology, 2000.
12. P. A. Parrilo and S. Lall. Semidefinite programming relaxations and algebraic optimization in control. European Journal of Control, 9(2-3):307-321, April 2003.
13. S. Prajna, A. Papachristodoulou, and P. A. Parrilo. Introducing sostools: A general purpose sum of squares programming solver. In Proceedings of the 41st IEEE Conference on Decision and Control, December 2002.