An improved LMI-based D-stability condition for polytopic uncertain systems

Proceedings of the IEEE International Symposium on Computer-Aided Control System Design

Volumn , Issue , 2004, Pages 237-242

  Liu, Yung Sheng ^a   Fang, Chun Hsiung ^a   Kau, Shih Wei ^a   Hong, Lin ^a  

^a NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

Author keywords

Linear matrix inequality; Parameter dependent Lyapunov matrix; Polytopic uncertainty; Robust D stability

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; LINEAR SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); THEOREM PROVING; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITY; PARAMETER-DEPENDENT LYAPUNOV MATRIX; POLYTOPIC UNCERTAINTY; ROBUST-D-STABILITY;

SYSTEMS ANALYSIS;

EID: 20344404179     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. F. Amato, M. Mattei, A. Pironti, "A note on quadratic stability of uncertain linear discrete-time systems," IEEE Trans. Automat. Control, vol. 43, no. 2, pp. 227-229, Feb. 1998.
2. F. Amato, M. Mattei, A. Pironti, "A robust stability problem for discrete-time systems subject to an uncertain parameter," Automatica, vol. 34, no. 4, pp. 521-523, Apr. 1998.
3. B. R. Barmish, "Necessary and sufficient conditions or quadratic stabilizability of an uncertain system," J. Optim. Theory Appl, vol. 46, pp. 399-408, Aug. 1985.
4. B. R. Barmish, New Tools for Robustness of Linear Systems, Macmillan Publishing Company, New York, 1994.
5. J. Bernussou, P. L. D. Peres, J. C. Geromel, "A linear programming oriented procedure for quadratic stabilization of uncertain systems," Systems and Control Letters, vol. 13, no. 1, pp. 65-72, July 1989.
6. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, USA 1994.
7. M. C. de Oliveira, J. Bernussou, J. C. Geromel, "A new discrete-time robust stability condition," Systems and Control Letters, vol. 37, no. 4, pp. 261-265, July 1999.
8. M. C. de Oliveira, J. C. Geromel, L. Hsu, "LMI characterization of structural and robust stability: the discrete-tune case," Linear Algebra Appl., vol. 296, no. 1-3, pp. 27-38, Apr. 1999.
9. P. J. de Oliveira, R. C. L. F. Oliveira, V. J. S. Leite, V. F. Montagner, and P. L. D. Peres, "LMI based robust stability conditions for linear uncertain systems: a numerical comparison," Proc. 41st IEEE CDC, Las Vegas, Nevada USA, vol. 1, pp. 644-649, Dec. 2002.
10. M. Dettori, C. W. Scherer, "Robust stability analysis for parameter-dependent systems using full block S-procedure," Proc. 37th IEEE CDC, Tampa, FL, vol. 3, pp. 2798-2799, Dec. 1998.
11. E. Feron, P. Apkarian, and P. Gahinet, "Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions," IEEE Trans. Automat. Control, vol. 41, no. 7, pp. 1041-1046, July 1996.
12. P. Gahinet P. Apkarian, M. Chilali, "Affine parameter-dependent Lyapunov functions and real parametric uncertainty," IEEE Trans. Automat. Control, Vol. 41, No. 3, pp. 436-442, Mar. 1996.
13. V. J. S. Leite, P. L. D. Peres, "An unproved LMI condition for robust 22-stability of uncertain polytopic systems," IEEE Trans. Automat. Control, vol. 48, no. 3, pp. 500-504, Mar. 2003.
14. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, "A new robust Instability condition for real convex polytopic uncertainty," Systems and Control Letters, vol. 40, no. 1, pp. 21-30, May 2000.
15. D. C. W. Ramos, P. L. D. Peres, "A less conservative LMI condition for the robust stability of discrete-time uncertain systems," Systems and Control Letters, vol. 43, no. 5, pp. 371-378, Aug. 2001.
16. D. C. W. Ramos, P. L. D. Peres, "An LMI condition for the robust stability of uncertain continuous-time linear systems," IEEE Trans. Automat. Control, vol. 47, no. 4, pp. 675-678, Apr. 2002.
17. A. Trofino, "Parameter dependent Lyapunov functions for a class of uncertain linear systems: an LMI approach," Proc. 38th IEEE CDC, Phoenix, AZ, vol. 3, pp. 2341-2346, Dec. 1999.