A polynomial approach for stability analysis of switched systems

Systems and Control Letters

Volumn 59, Issue 2, 2010, Pages 98-104

  Mojica Nava, E ^a,b   Quijano, N ^a   Rakoto Ravalontsalama, N ^b   Gauthier, A ^a  

^a UNIVERSIDAD DE LOS ANDES   (Colombia)

^b ECOLE DES MINES DE NANTES   (France)

Author keywords

Common Lyapunov function; Dissipation inequalities; Polynomial systems; Sum of squares decomposition; Switched systems

Indexed keywords

COMMON LYAPUNOV FUNCTIONS; DISSIPATION INEQUALITY; POLYNOMIAL SYSTEMS; SUM OF SQUARES DECOMPOSITIONS; SWITCHED SYSTEM;

DIFFERENTIAL EQUATIONS; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; NONLINEAR SYSTEMS; POLYNOMIALS; SWITCHING SYSTEMS;

SYSTEM STABILITY;

EID: 75249098345     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2009.12.004     Document Type: Article

References (23)

1. Liberzon D. Switching in Systems and Control (2003), Birkhauser, Boston
2. Lin H., and Antsaklis P. Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Transactions on Automatic Control 54 2 (2009) 308-322
3. Dayawansa W., and Martin C. A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Transactions on Automatic Control 44 4 (1999) 751-760
4. Mancilla-Aguilar J., and Garcia R. A converse Lyapunov theorem for nonlinear switched systems. Systems & Control Letters 41 1 (2000) 67-71
5. Vu L., and Liberzon D. Common Lyapunov functions for families of commuting nonlinear systems. Systems & Control Letters 54 (2005) 405-416
6. E. Mojica-Nava, R. Meziat, N. Quijano, A. Gauthier, N. Rakoto-Ravalontsalama, Optimal control of switched systems: A polynomial approach, in: Proceedings of the 17th IFAC World Congress, 2008, pp. 7808-7813
7. E. Mojica-Nava, N. Quijano, A. Gauthier, N. Rakoto-Ravalontsalama, Stability analysis of switched polynomial systems using dissipation inequalities, in: Proceedings of the 47th IEEE Conference on Decision and Control, 2008
8. Ebenbauer C., and Allgöwer F. Stability analysis of constrained control systems: An alternative approach. Systems & Control Letters 56 (2007) 93-98
9. Papachristodoulou A., and Prajna S. Analysis of non-polynomial systems using the sum of squares decompostion. Positive Polynomials in Control (2005), Springer 23-43
10. Kunkel P., and Mehrmann V. Stability properties of differential-algebraic equations and spin-stabilized descretizations. Electronic Transactions on Numerical Analysis 26 (2007) 385-420
11. Ebenbauer C., and Allgöwer F. Analysis and design of polynomial control systems using dissipation inequalities and sum of squares. Computers and Chemical Engineering 30 (2006) 1590-1602
12. S. Prajna, A. Papachristodoulou, Analysis of switched and hybrid systems-Beyond piecewise quadratic methods, in: Proceedings of the American Control Conference, 2003, pp. 2779-2784
13. Willems J. Dissipative dynamical systems Part I: General theory. Archive for Rational Mechanics and Analysis 45 (1972) 321-351
14. Zhao J., and Hill D. Passivity and stability of switched systems: A multiple storage function method. Systems & Control Letters 57 (2008) 158-164
15. M. Zefran, F. Bullo, M. Stein, A notion of passivity for hybrid systems, in: Proceedings of the 40th IEEE Conference on Decision and Control, 2001, pp. 768-773
16. Lasserre J.B. An explicit equivalent positive semidefinite program for nonlinear 0-1 programs. SIAM Journal on Optimization 12 (2002) 756-769
17. Burden R., and Faires J.D. Numerical Analysis (1985), PWS, Boston
18. S. Prajna, A. Papachristodoulou, On the construction of Lyapunov functions using the sum of squares decomposition, in: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, pp. 3482-3487
19. P. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, Ph.D. Thesis, California Institute of Technology, 2000
20. A. Papachristodoulou, S. Prajna, P. Parrilo, Introducing SOSTOOLS: A general purpose sum of squares programming solver, in: Proceedings of the IEEE Conference on Decision and Control, 2002, pp. 741-746
21. Li Z., Qiao Y., Qi H., and Cheng D. Stability of switched polynomial systems. Journal of Systems Science and Complexity 21 3 (2008) 362-377
22. Savageau M., and Voit E. Recasting nonlinear differential equations as S-systems: A canonical nonlinear form. Mathematical Biosciences 87 1 (1987) 83-115
23. Åström K., Aracil J., and Gordillo F. A family of smooth controllers for swinging up a pendulum. Automatica 44 7 (2008) 1841-1848