Relation between exponential stability and input-to-state stability of time-delay systems

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 4919-4920

  Yeganefar, Nima ^a   Dambrine, Michel ^b   Yeganefar, Nader ^c  

^a ECOLE CENTRALE DE LILLE   (France)

^b UNIVERSITÉ DE VALENCIENNES   (France)

^c AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Exponential stability; Input to state stability; Lyapunov Krasovskii theorem; Nonlinear time delay systems

Indexed keywords

AEROSPACE ENGINEERING; DELAY CONTROL SYSTEMS; FARM BUILDINGS; FEEDBACK CONTROL; TIME DELAY;

ARBITRARY SIZE; EXPONENTIAL STABILITY; EXPONENTIALLY STABLE; INPUT-TO-STATE (ISS) STABILITY; INPUT-TO-STATE-STABLE (ISS); LYAPUNOV; TIME DELAY SYSTEMS; TRIVIAL SOLUTIONS; UNFORCED SYSTEM;

SYSTEM STABILITY;

EID: 46449118360     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282609     Document Type: Conference Paper

References (13)

1. E. Sontag, "the ISS philosophy as a unifuing framework for stability-like behavior," Nonlinear Control in the Year 2000 (Volume 2), pp. 443-468, 2000.
2. _, "Smooth stabilization implies coprime factorization," IEEE Trans. Aut. Control vol. vol. 34(4), pp. 435-443, 1989.
3. A. Teel, "Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem," IEEE Trans. Aut. Control vol. vol. 43(7), pp. 960-964, 1998.
4. P. Pepe and Z.-P. Jiang, "A Lyapunov-Krasovskii methodology for ISS of time-delay systems," in Proc. Of the 44th IEEE CDC and ECC. Seville, Spain, 2005.
5. D. Liberzon, "Quantization, time delays, and nonlinear stabilization," IEEE Trans. Aut. Control.
6. A. Seuret, M. Dambrine, and J.-P Richard, "Robust exponential stabilization for systems with time-varying delays," in TDS'04, IFAC Workshop Time-Delay Systems. Leuven, Belgium, Sept. 2004.
7. I. Polushin and H. Marquez, "Stabilization of bilaterally ontrolled teleoperators with communication delay: an ISS approach," Systems and Control Letters, vol. vol. 24, pp. 351-359, 2003.
8. H. Khalil, Nonlinear Systems. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 2002.
9. V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations. Kluwer Acad. Pub., 1992.
10. P Pepe and Z.-P. Jiang, "A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems," Systems & Control Letters, vol. vol. 55(12), pp. 1006-1014, 2006.
11. T. Burton, Stability and periodic solutions of ordinary and functional differential equations. Academic Press, Inc., 1985.
12. T. Yoshizawa, Stability Theory by Liapunov's Second Method. Tokyo: The Mathematical Society of Japan, 1966.
13. N. Krasovskii, Stability of motion. Stanford University Press., 1963.