Criteria for robust stability and stabilization of uncertain linear systems with state delay

Automatica

Volumn 33, Issue 9, 1997, Pages 1657-1662

  Li, Xi ^b   De Souza, Carlos E ^a  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b NONE

Author keywords

Linear matrix inequalities; Robust stability; Robust stabilizability; State feedback; Time delay systems

Indexed keywords

CONTROL SYSTEM ANALYSIS; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; STATE SPACE METHODS; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

TIME VARYING STATE DELAY; UNCERTAIN LINEAR SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0031222129     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(97)00082-4     Document Type: Article

References (25)

1. Brierley, S. D., J. N. Chiasson, E. B. Lee and S. H. Zak (1982). On stability independent of delay for linear systems. IEEE Trans. Automat. Control, AC-27, 252-254.
2. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in Systems and Control Theory. Studies in Applied Mathematics, Vol. 15, SIAM, Philadelphia.
3. Chen, J., D. Xu and B. Shafai (1995). On sufficient conditions for stability independent of delay. IEEE Trans. Automat. Control, 40, 1675-1680.
4. Cheres, E. S., S. Gutman and Z. J. Palmor (1989). Robust stabilization of uncertain dynamic systems including state delay. IEEE Trans. Automat. Control, 34, 1199-1203.
5. Hale, J. and S. M. V. Lunel (1993). Introduction to Functional Differential Equations. Springer, New York.
6. Lewis, R. M. and B. D. O. Anderson (1980). Necessary and sufficient conditions for delay independent stability of linear autonomous systems. IEEE Trans. Automat. Control, AC-25, 735-739.
7. Luo J. S., A. Johnson and P. P. J. van den Bosch (1995) Delay-independent robust stability of uncertain linear systems Systems Control Lett.24, 33-39
8. Mahmoud, M. S. and N. F. Al-Muthairi (1994). Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties. IEEE Trans. Automat. Control, 39, 2135-2139.
9. Malek-Zavarei, M. and M. Jamshidi (1987). Time Delay Systems: Analysis, Optimization and Applications. North-Holland.
10. Mori, T. and H. Kokame (1989). Stability of x(t) = Ax(t) + Bx(t - τ). IEEE Trans. Automat. Control, 34, 460-462.
11. Nesterov, Yu. and A. Nemirovsky (1994). Interior Point Polynomial Methods in Convex Programming. Studies in Applied Mathematics, Vol. 13, SIAM, Philadelphia.
12. Niculescu, S. I., C. E. de Souza, J. M. Dion and L. Dugard (1994a). Robust stability and stabilization of uncertain linear systems with state delay: Single delay case (I). Proc. IFAC Symp. on Robust Control Design, Rio de Janeiro, Brazil, September 1994.
13. Niculescu, S. I., C. E. de Souza, J. M. Dion and L. Dugard (1994b). Robust stability and stabilization of uncertain linear systems with state delay: Multiple delays case (II). Proc. IFAC Symp. on Robust Control Design, Rio de Janeiro, Brazil, September 1994.
14. Niculescu, S. I., L. Dugard and J. M. Dion (1995a). Stabilité et stabilisation robustes des systèmes à retard. Proc. Journées Robustesse, Toulouse, France, February 1995.
15. Niculescu, S. I., A. Trofino Neto, J. M. Dion and L. Dugard (1995b). Delay dependent stability of linear systems with delayed state: An LMI approach. Proc. 34th IEEE Conf. Decision and Control, New Orleans, LA, December 1995.
16. Phoojaruenchanachai, S. and K. Furuta (1992). Memoryless stabilization of uncertain linear systems including time-varying state delays. IEEE Trans. Automat. Control, 37, 1022-1026.
17. Shen, J. C., B. -S. Chen and F. -C. Kung (1991). Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach. IEEE Trans. Automat. Control, 36, 638-640.
18. Su, J. -H. (1994). Further results on the robust stability of linear systems with a single time delay. Systems Control Lett., 23, 375-379.
19. Su, T. J. and C. G. Huang (1992). Robust stability of delay dependence for linear uncertain systems. IEEE Trans. Automat. Control, 37, 1656-1659.
20. Thowsen, A. (1983). Uniform ultimate boundness of the solutions of uncertain dynamic delay systems with state-dependent and memoryless feedback control. Int. J. Control, 37, 1135-1143.
21. Verriest, E. I., M. K. H. Fan and J. Kullstam (1993). Frequency domain robust stability criteria for linear delay systems. Proc. 32nd IEEE Conf. Decision and Control, San Antonio, TX, December 1993.
22. Wang, S. S., B. S. Chen and T. P. Lin (1987). Robust stability of uncertain time-delay systems. Int. J. Control, 46, 963-976.
23. Wang, Y., L. Xie and C. E. de Souza (1992). Robust control of a class of uncertain nonlinear systems. Systems Control Lett., 19, 139-149.
24. Xie, L. and C. E. de Souza (1993). Robust stabilization and disturbance attenuation for uncertain delay systems. Proc. 1993 European Control Conf., Gröningen, The Netherlands, June 1993.
25. Xu, B. (1994) Comments on Robust stability of delay dependence for linear uncertain systems. IEEE Trans. Automat. Control, 39, 2365.