On the stability analysis of nonlinear systems using polynomial Lyapunov functions

Mathematics and Computers in Simulation

Volumn 76, Issue 5-6, 2008, Pages 316-329

  Bouzaouache, Hajer ^a   Braiek, Naceur Benhadj ^a  

^a UNIVERSITY OF CARTHAGE   (Tunisia)

Author keywords

Kronecker product; LMIs; Nonlinear system; Polynomial lyapunov function; Stability

Indexed keywords

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; POLYNOMIALS; PROBLEM SOLVING; ROBUST CONTROL; SEARCH ENGINES;

COMPUTATIONAL IMPLEMENTATION; KRONECKER PRODUCT; POLYNOMIAL LYAPUNOV FUNCTION;

NONLINEAR SYSTEMS;

EID: 37049002038     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.04.001     Document Type: Article

References (21)

1. Bbenhadj Braiek E., Rotella F., and Benrejeb M. Algebraic criteria for global stability analysis of nonlinear systems. SAMS J. 17 (1995) 211-227
2. Benhadj Braiek E. A Kronecker product approach of stability domain determination for nonlinear continuous systems. SAMS J. 11 (1996) 11-16
3. Benhadj Braiek E., and Rotella F. Logid: a non linear systems identification software in mModelling and Simulation of systems. IMACS, Ed. P. Breedveld (1989) 211-217
4. M. Benrejeb, Sur l'analyse et la synthèse de processus complexes hiérarchisés. Applications aux systèmes singulièrement perturbés, Thèse de docteur ès sciences physiques, no. 479, Lille, 1980.
5. P.A. Bliman, Lyapunov equation for the stability of 2D systems, Rapport de recherche, no. 4014 INRIA, 2000.
6. Borne P., and Gentina J.C. On the Stability of Large Nonlinear Systems (1974), Joint Aut. Cont. Conf., Austin, Texas
7. Borne P., and Benrejeb M. On the stability of a class of interconnected systems. Application to the forced Working conditions. Proceedings of the 4th IFAC Symposium MTS. Fredericton, Canada (1977)
8. Bouzaouache H., Benhadj E., and Braiek. An approach for order reduction of nonlinear singularly perturbed systems. 15ème IMACS, Berlin, Germany 2 (1997) 27-32
9. Bouzaouache H., Benhadj Braiek E., and Benrejeb M. A reduced optimal control for nonlinear singularly perturbed systems. Syst. Anal. Model. Simulation J. 43 (2003) 75-87
10. Boyd S., and Yang Q. Structured and simultaneous Lyapunov for system stability problems. Int. J. Control 49 6 (1989) 2215-2240
11. Boyd S., Ghaoui L.E., and Balakrishnan F.E. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia
12. Brewer J.W. Kronecker product and matrix calculus in system theory. IEEE Trans. Circ. Syst. 25 9 (1978) 772-781
13. G. Chesi, A. Garulli, A. Tesi, A. Vicino, Homogeneous polynomial Lyapunov functions for robust stability analysis of LFR systems, DII-Technical Report 23, 2002.
14. G. Chesi, A. Garulli, A. Tesi, A. Vicino, Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach, DII- Technical Report 23, 2002.
15. Gleria I.M., Figueiredo A., and Rocha Filho T.M. A numerical method for the stability analysis of quasi-polynomial vector fields. Nonlinear A 52 (2003) 329-342
16. Johansen T.A. Computation of Lyapunov function for smooth nonlinear systems using convex optimisation. Automatica 36 (2000) 1617-1626
17. Sing Kiong N., and FU M. Global quadratic stabilization of a class of nonlinear systems. Int. J. Robust Nonlinear Control. 8 (1998) 483-497
18. Narandra K.S., and Balakrishnan J. A common Lyapunov function for stable LTI systems with commuting A-matrices. IEEE Trans. Aut. Cont. 39 12 (1994) 2469-2471
19. Papachristodoulou A., and Prajna S. On the construction of Lyapunov functions using the sum of squares decomposition. Proceeding of IEEE Conf. Decision Control (2002)
20. Rotella F., and Dauphin-tanguy G. Non-linear systems: identification and optimal control. Int. J. Control 48 2 (1988) 525-544
21. Zelentsovsky A.L. Non quadratic Lyapunov functions for robust stability analysis of linear uncertain systems. IEEE Trans. Automat. Control 39 1 (1994)