Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions

Automatica

Volumn 43, Issue 2, 2007, Pages 309-316

  Chesi, G ^a   Garulli, A ^a   Tesi, A ^b   Vicino, A ^a  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Bounded variation rate uncertainty; LMI; Lyapunov function; Polytopic system; Robust stability

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; POLYNOMIALS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

BOUNDED VARIATION RATE UNCERTAINTY; LINEAR MATRIX INEQUALITIES (LMI); POLYTOPIC SYSTEMS; TIME-INVARIANT PERTURBATIONS;

TIME VARYING CONTROL SYSTEMS;

EID: 33845934993     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.08.024     Document Type: Article

References (33)

1. Almeida H.L.S., Bhaya A., Falcao D.M., and Kaszkurewicz E. A team algorithm for robust stability analysis and control design of uncertain time-varying linear systems using piecewise quadratics Lyapunov functions. International Journal of Robust and Nonlinear Control 11 (2001) 357-371
2. Barmish B.R. New tools for robustness of linear systems (1994), Macmillan Publishing Company, New York
3. Blanchini F. Nonquadratic Lyapunov functions for robust control. Automatica 31 (1995) 451-461
4. Blanchini F., and Miani S. A universal class of smooth functions for robust control. IEEE Transactions on Automatic Control 44 3 (1999) 641-647
5. Bliman, P.-A. (2002). Nonconservative LMI approach to robust stability for systems with uncertain scalar parameters. Proceedings of 41st IEEE CDC (pp. 305-310). Las Vegas, Nevada.
6. Bliman P.-A. A convex approach to robust stability for linear systems with uncertain scalar parameters. SIAM Journal on Control and Optimization 42 6 (2004) 2016-2042
7. Boyd S., El Ghaoui L., Feron E., and Balakrishnan V. Linear matrix inequalities in system and control theory (1994), SIAM, Philadelphia
8. Brayton R.K., and Tong C.H. Stability of dynamical systems: A constructive approach. IEEE Transactions on Circuits and Systems 26 (1979) 224-234
9. Chesi G., Garulli A., Tesi A., and Vicino A. Homogeneous Lyapunov functions for systems with structured uncertainties. Automatica 39 6 (2003) 1027-1035
10. Chesi, G., Garulli, A., Tesi, A., Vicino, A. (2003b). Robust stability for polytopic systems via polynomially parameter-dependent Lyapunov functions. 42nd IEEE CDC (pp. 4670-4675). Maui, Hawaii.
11. Chesi G., Garulli A., Tesi A., and Vicino A. Solving quadratic distance problems: An LMI-based approach. IEEE Transactions on Automatic Control 48 2 (2003) 200-212
12. Chesi, G., Garulli, A., Tesi, A., & Vicino, A. (2004a). Parameter-dependent homogeneous Lyapunov functions for robust stability of linear time-varying systems. 43rd IEEE CDC (pp. 4095-4100). Paradise Island, Bahamas.
13. Chesi G., Garulli A., Tesi A., and Vicino A. Robust analysis of LFR systems through homogeneous polynomial Lyapunov functions. IEEE Transactions on Automatic Control 49 7 (2004) 1211-1216
14. Chesi, G., Garulli, A., Tesi, A., & Vicino, A. (2005). An LMI-based technique for robust stability analysis of linear systems with polynomial parametric uncertainties. In D. Henrion, A. Garulli (Eds.), Positive polynomials in control, Lecture Notes in Control and Information Sciences, Vol. 312, (pp. 87-101). London: Springer.
15. Chesi, G., Tesi, A., Vicino, A., & Genesio, R. (1999). On convexification of some minimum distance problems. 5th European Control Conf. (F0531.pdf), Karlsruhe, Germany.
16. Choi M., Lam T., and Reznick B. Sums of squares of real polynomials. Proceedings of symposia in pure mathematics (1995) 103-126
17. Dasgupta S., Chockalingam G., Anderson B.D.O., and Fu M. Lyapunov functions for uncertain systems with applications to the stability of time varying systems. IEEE Transactions on Automatic Control 41 (1994) 93-106
18. Gahinet P., Apkarian P., and Chilali M. Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Transactions on Automatic Control 41 3 (1996) 436-442
19. Geromel J.C., and Colaneri P. Robust stability of time varying polytopic systems. Systems and Control Letters 55 1 (2005) 81-85
20. Henrion D., and Lasserre J.-B. Convergent relaxations of polynomial matrix inequalities and static output feedback. Transactions on Automatic Control 51 2 (2006) 192-202
21. Hol, C., and Scherer, C. (2005). Sum of squares relaxations for robust polynomial semi-definite programs. In Proceedings of 15th IFAC World Congress, Prague.
22. Horisberger H.P., and Belanger P.R. Regulators for linear time invariant plants with uncertain parameters. IEEE Transactions on Automatic Control 21 5 (1976) 705-708
23. Jarvis-Wloszek, Z., Packard, A. K. (2002). An LMI method to demonstrate simultaneous stability using non-quadratic polynomial Lyapunov functions. Proceedings of 41st IEEE CDC(pp. 287-292). Las Vegas, Nevada.
24. Leite V.J.S., and Peres P.L.D. An improved LMI condition for robust D-stability of uncertain polytopic systems. IEEE Transactions on Automatic Control 48 3 (2003) 500-504
25. Montagner, V. F., Peres, P. L. D. (2003). A new LMI condition for the robust stability of linear time-varying systems. Proceedings of 42nd IEEE CDC (pp. 6133-6138). Maui, Hawaii.
26. Narendra K.S., and Taylor J.H. Frequency domain criteria for absolute stability (1973), Academic Press Inc, New York
27. Parrilo, P. A. (2000). Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California Institute of Technology.
28. Peaucelle D., Arzelier D., Bachelier O., and Bernussou J. A new robust D-stability condition for real convex polytopic uncertainty. Systems and Control Letters 40 (2000) 21-30
29. Trofino, A. (1999). Parameter dependent Lyapunov functions for a class of uncertain linear systems: A LMI approach. Proceedings of 38th IEEE CDC (pp. 2341-2346). Phoenix, Arizona.
30. Šiljak D. Nonlinear Systems: Parametric Analysis and Design (1969), Wiley, New York
31. Wu F., and Prajna S. Sos-based solution approach to polynomial LPV system analysis and synthesis problems. International Journal of Control 78 8 (2005) 600-611
32. Xie L., Shishkin S., and Fu M. Piecewise Lyapunov functions for robust stability of linear time-varying systems. Systems and Control Letters 31 (1997) 165-171
33. Zelentsovsky A.L. Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems. IEEE Transactions on Automatic Control 39 1 (1994) 135-138