Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach

IEEE Transactions on Automatic Control

Volumn 42, Issue 8, 1997, Pages 1144-1148

  Li, Xi ^a   De Souza, Carlos E ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

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

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DIFFERENTIAL EQUATIONS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); STATE SPACE METHODS; SYSTEM STABILITY;

LINEAR MATRIX INEQUALITY; TIME DELAY SYSTEMS;

DELAY CONTROL SYSTEMS;

EID: 0031200034     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.618244     Document Type: Article

References (17)

1. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in systems and control theory," in Studies in Applied Mathematics, vol. 15. Philadelphia, PA: SIAM, 1994.
2. E. S. Cheres, S. Gutman, and Z. J. Palmor, "Robust stabilization of uncertain dynamic systems including state delay," IEEE Trans. Automat. Contr., vol. 34, pp. 1199-1203, 1989.
3. J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
4. M. S. Mahmoud and N. F. Al-Muthairi, "Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties," IEEE Trans. Automat. Contr., vol. 39, pp. 2135-2139, 1994.
5. M. Malek-Zavarei and M. Jamshidi, Time Delay Systems: Analysis, Optimization and Applications. North-Holland: 1987.
6. Y. Nesterov and A. Nemirovsky, "Interior point polynomial methods in convex programming," in Studies in Applied Mathematics, vol. 13. Philadelphia, PA: SIAM, 1994.
7. S. I. Niculescu, C. E. de Souza, J. M. Dion, and L. Dugard, "Robust stability and stabilization of uncertain linear systems with state delay: Single delay case," in Proc. IFAC Symp. Robust Contr. Design, Rio de Janeiro, Brazil, Sept. 1994.
8. _, "Robust stability and stabilization of uncertain linear systems with state delay: Multiple delays case," in Proc. IFAC Symp. Robust Contr. Design, Rio de Janeiro, Brazil, Sept. 1994.
9. S. Phoojaruenchanachai and K. Furuta, "Memoryless stabilization of uncertain linear systems including time-varying state delays," IEEE Trans. Automat. Contr., vol. 37, pp. 1022-1026, 1992.
10. J. C. Shen, B.-S. Chen, and F.-C. Kung, "Memoryless stabilization of uncertain dynamic delay systems Riccati equation approach," IEEE Trans. Automat. Contr., vol. 36, pp. 638-640, 1991.
11. J.-H. Su, "Further results on the robust stability of linear systems with a single time delay," Syst. Contr. Lett., vol. 23, pp. 375-379, 1994.
12. T. J. Su and C. G. Huang, "Robust stability of delay dependence for linear uncertain systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1656-1659, 1992.
13. E. I. Verriest, M. K. H. Fan, and J. Kullstam, "Frequency domain robust stability criteria for linear delay systems," in Proc. 32nd IEEE Conf. Decision Contr., San Antonio, TX, Dec. 1993.
14. S. S. Wang, B. S. Chen, and T. P. Lin, "Robust stability of uncertain time-delay systems," Int. J. Contr., vol. 46, pp. 963-976, 1987.
15. Y. Wang, L. Xie, and C. E. de Souza, "Robust control of a class of uncertain nonlinear systems," Syst. Contr. Lett., vol. 19, pp. 139-149, 1992.
16. L. Xie and C. E. de Souza, "Robust stabilization and disturbance attenuation for uncertain delay systems," in Proc. 1993 European Contr. Conf., Groningen, The Netherlands, July 1993.
17. B. Xu, "Comments on 'Robust stability of delay dependence for linear uncertain systems,'" IEEE Trans. Automat. Contr., vol. 39, p. 2365, 1994.