Stability region analysis for uncertain nonlinear systems

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 1693-1698

  Topcu, Ufuk ^a   Packard, Andrew ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; NONLINEAR SYSTEMS; OPTIMIZATION; PERTURBATION TECHNIQUES; POLYNOMIALS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

COMPUTATIONAL TOOLS; EQUILIBRIUM POINTS;

SYSTEM STABILITY;

EID: 62749158257     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434914     Document Type: Conference Paper

References (19)

1. A. Ben-Tal and A. Nemirovski. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. MPS-SIAM Series on Optimization, 2001.
2. G. Chesi. Estimating the domain of attraction of uncertain poynomial systems. Automatica, 40:1981-1986, 2004.
3. G. Chesi, A. Garulli, A. Tesi, and A. Vicino. LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems. Int. J. Robust Nonlinear Control, 15:35-49, 2005.
4. E. J. Davison and E. M. Kurak. A computational method for determining quadratic Lyapunov functions for nonlinear systems. Automatica, 7:627-636, 1971.
5. R. Genesio, M. Tartaglia, and A. Vicino. On the estimation of asymptotic stability regions: State of the art and new proposals. IEEE Transaction on Automatic Control, 30(8):747-755, 1985.
6. D. Henrion and M. Šebek. Overcoming nonconvexity in polynomial robust control design. In Proc. Symp. Math. Theory of Networks and Systems, Leuven, Belgium, 2006.
7. rd edition, 2002.
8. M. Kočvara and M. Stingl. PENBMI User's Guide (Version 2.0), available from http://www.penopt.com. 2005.
9. A. Paice and F. Wirth. Robustness analysis of domains of attraction of nonlinear systems. In Proc. of the Mathematical Theory of Networks and Systems, pages 353-356, Padova, Italy, 1998.
10. A. Papachristodoulou. Scalable analysis of nonlinear systems using convex optimization. Ph.D. dissertation, Caltech, January 2005.
11. A. Papachristodoulou and S. Prajna. Analysis of non-polynomial systems using the sum of squares decomposition. In D. Henrion and A. Garulli, editors, Positive Polynomials in Control, pages 23-43. Springer-Verlag, 2005.
12. P. Parrilo. Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming Series B, 96(2):293-320, 2003.
13. W. Tan. Nonlinear control analysis and synthesis using sum-of-squares programming. Ph.D. dissertation, UC, Berkeley, May 2006.
14. W. Tan and A. Packard. Stability region analysis using sum of squares programming. In Proc. American Control Conf, pages 2297-2302, Minneapolis, MN, 2006.
15. U. Topcu, A. Packard, and P. Seiler. Local stability analysis using simulations and sum-of-squares programming, 2006. submitted to Automatica, paper number: 6817.
16. U. Topcu, A. Packard, P. Seiler, and T. Wheeler. Stability region analysis using simualtions and sum-of-squares programming. In Proc. American Control Conf., New York, NY, 2007.
17. A. Vannelli and M. Vidyasagar. Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems. Automatica, 21(1):69-80, 1985.
18. nd edition, 1993.
19. T.-C. Wang, S. Lall, and M. West. Polynomial level-set methods for nonlinear dynamical systems analysis. In Proc. Allerton Conf. on Communication, Control, and Computing, Allerton, IL, 2005.