Stability analysis and controller synthesis for parameter-dependent polynomial nonlinear systems

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 6015-6020

  Zhao, Dan ^a   Wang, Jian Liang ^a   Poh, Eng Kee ^b   Liao, Fang ^c  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b DSO NATIONAL LABORATORIES   (Singapore)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; DIFFERENTIAL EQUATIONS; FEEDBACK; LYAPUNOV FUNCTIONS; MILITARY DATA PROCESSING; NONLINEAR PROGRAMMING; NONLINEAR SYSTEMS; OPTICAL BISTABILITY; POLYNOMIAL APPROXIMATION; POLYNOMIALS; STABILITY; SYSTEM STABILITY; TELECOMMUNICATION NETWORKS;

(001) PARAMETER; CLOSED-LOOP SYSTEMS; CONTROLLER DESIGNS; CONTROLLER SYNTHESIS; FEEDBACK CONTROLLERS; LYAPUNOV; LYAPUNOV STABILITY THEOREMS; OPTIMIZ ATION PROBLEMS; PAPER ADDRESSES; POLYNOMIAL VECTOR FIELDS; SEMI DEFINITE PROGRAMMING (SDP); STABILITY ANALYSIS (IGC: E5/E13); SUFFICIENT CONDITIONS (SC); SUM OF SQUARES (SOS); SYNTHESIS (OF CHIRAL IONIC LIQUIDS); SYNTHESIS PROBLEMS;

STATE FEEDBACK;

EID: 46449112172     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282615     Document Type: Conference Paper

References (20)

1. A. Isidori, Nonlinear Control Systems, Springer Verlag, New York; 1995.
2. P. A. Parrilo, Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, California Institute of Technology, PhD thesis, 2000.
3. Weehong Tan, Nonlinear Control Analysis and Synthesis using Sumof-Squares Progrmming, University of California, Berkeley, PhD thesis, 2006.
4. W. H. Tan and A. Packard, "Stability Region Analysis using Sum of Squares Programming", In Proceedings of the American Control Conferrence, Minneapolis, Minnesota, USA, 2006, pp 2297-2302.
5. D. Henrion and A. Garulli, Positive Polynomials in Control, Springer, Berlin; 2005.
6. H. K. Khalil, Nonlinear Systems (Third Edition), Prentice Hall, NJ; 2002.
7. J. Bochnak, M. Coste and M.-F. Roy, Real Algebraic Geometry, Springer; 1998.
8. C. Ebenbauer and T. Raff and F. Allgöwer, "A Duality-based LPV Approach to Polynomial State Feedback Design", In Proceedings of the American Control Conference, Portland, OR, 2005, pp 703-708.
9. H. Ichihara and E. Nobuyama, "Minimax Polynomial Optimization by using Sum of Squares Relaxation and its Application to Robust Stability Analysis of Parameter-dependent Systems", In Proceedings of the American Control Conferrence, Portland, OR, 2005, pp 3433-3434.
10. P. Kokotović and M. Arcak, Constructive Nonlinear Control: A Historical Perspective, Automatica, vol. 37, 2001, pp 637-662.
11. K. Krishnaswamy, G. Papageorgiou, S. Glavaski and A. Papachristodoulou, "Analysis of Aircraft Pitch Axis Stability Augmentation System using Sum of Squares Optimization", In Proceedings of the American Control Conferrence, Portland, OR, 2005, pp 1497-1502.
12. F. Liao, J. L. Wang and G. H. Yang, "Output-feedback Tracking Control of a Set of Affine Parameter-dependent Systems", In Proceedings of the IEEE Conference on Decision and Control, Orlando, Florida, 2001, pp 4891-4896.
13. A. Papachristodoulou, "Analysis of Nonlinear Time Delay Systems using the Sum of Squares Decomposition", In Proceedings of the American Control Conferrence, Boston, Massachusetts, 2004, pp 4153-4158.
14. A. Papachristodoulou and S. Prajna, "On the Construction of Lyapunov Functions using the Sum of Squares Decomposition", In Proceedings of the IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, pp 3482-3487.
15. S. Prajna and A. Papachristodoulou, "Analysis of Switched and Hybrid Systems-beyond Piecewise Quadratic Methods", In Proceedings of the American Control Conferrence, Denver, Colorado, 2003, pp 2779-2784.
16. S. Prajna, A. Papachristodoulou and P. A. Parrilo, "Introducing SOS-TOOLS: A General Purpose Sum of Squares Programming Solver", In Proceedings of the IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002, pp 741-746.
17. S. Prajna, A. Papachristodoulou, P. Seiler and P. A. Parrilo, SOSTOOLS-Sum of Squares Optimization Toolbox, User's Guide, Version 2.00, Available at http://www.cds.caltech.edu/sostools and http://control.ee.ethz. ch/~parrilo/sostools, 2004.
18. S. Prajna, A. Papachristodoulou, P. Seiler and P. A. Parrilo, SOS-TOOLS: Control Applications and New Developments, IEEE International Symposium on Computer Aided Control Systems Design, 2004, pp 315-320.
19. S. Prajna, A. Papachristodoulou and F. Wu, "Nonlinear Control Synthesis by Sum of Squares Optimization: A Lyapunov-based Approach", In Proceedings of the Asian Control Conference, 2004, pp 157-165.
20. Z. Jarvis-Wloszek, R. Feeley, W. H. Tan, K. P. Sun and A. Packard, "Some Controls Applications of Sum of Squares Programming", In Proceedings of the IEEE Conference on Decision and Control, 2003, pp 4676-4681.