Stability of some linear systems with delays

IEEE Transactions on Automatic Control

Volumn 44, Issue 5, 1999, Pages 984-989

  Kolmanovskii, Vladimir B ^a   Richard, Jean Pierre ^b,c  

^a Russian Academy of Sciences ^*  (Russian Federation)

^b ECOLE CENTRALE DE LILLE   (France)

^c ECOLE CENTRALE DE LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DISCRETE TIME CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; LINEAR EQUATIONS; LYAPUNOV METHODS; RICCATI EQUATIONS; SYSTEM STABILITY;

DELAY-DEPENDENT STABILITY CONDITIONS; HEREDITARY SYSTEMS; LYAPUNOV-KRASSOVSKII METHOD;

DELAY CONTROL SYSTEMS;

EID: 0032630709     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.763213     Document Type: Article

References (16)

1. V. B. Kolmanovskii and L. E. Shaikhet, "Control of systems with after effect," American Math. Soc., RI, vol. 157, p. 359, 1996.
2. V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations New York: Academic, 1986.
3. E. I. Verriest, "Riccati type conditions for robust stability of delay systems," in Proc. MTNS, St. Louis, MO, 1996.
4. M. Malek-Zavarei and M. Jamshidi, Time-Delay Systems. Amsterdam, The Netherlands, North-Holland, 1996.
5. M. Slemrod and E. F. Infante, "Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues," J. Math. Anal. Appl., vol. 38, pp. 399-415, 1972.
6. V. B. Kolmanovskii, "Stability of some nonlinear functional differential equations," J. Nonlinear Differential Equations and Appl., no. 2, pp. 185-198, 1995.
7. L. Dugard and E. I. Verriest, Eds., "Stability and control of time-delay systems," in Lect. Notes Contr. Inform. Sci., no. 228. New York: Springer, 1997.
8. 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.
9. S. Boyd, L. El Ghaoui, E. Feran, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," SIAM Studies in Appl. Math., vol. 15, 1994.
10. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations. New York: Springer, 1993.
11. A. Bellen, V. B. Kolmanovskii, L. Torelli, and R. Vermiglio, "About stability of some functional differential equations of neutral type," J. Math. Anal. and Appl., vol. 189, pp. 59-94, 1995.
12. A. Goubet-Bartholoméüs, M. Dambrine, and J. P. Richard, "Stability of perturbed systems with time-varying delay," Syst. Contr. Lett., no. 31, pp. 155-163, 1997.
13. M. Dambrine and J. P. Richard, "Stability and stability domains analysis for nonlinear differential-difference equations," Dynamic Syst. Appl., vol. 3, pp. 369-378, 1994.
14. J. P. Richard, A. Goubet-Bartholoméüs, P. A. Tchangani, and M. Dambrine, "Nonlinear delay systems Tools for a quantitative approach to stabilization," Stability and Control of Time-Delay Systems, Lect. Notes in Contr. Inform. Sci., no. 228. New York: Springer, 1997, ch. 10.
15. H. Tokumaru, N. Adachi, and T. Amemiya, "Macroscopic stability of interconnected systems," in 6th IFAC Conf., paper ID 44.4, 1975, preprints.
16. T. Mori, "Criteria for asymptotic stability of linear time delay systems," IEEE Trans. Automat. Contr., vol. 30, pp. 158-160, 1985.