On input-to-state stability for nonlinear systems with delayed feedbacks

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 4804-4809

  Mazene, Frederic ^a   Malisoff, Michael ^b   Lin, Zongli ^c  

^a INRIA   (France)

^b LOUISIANA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

(MIN ,MAX ,+) FUNCTIONS; CASCADE SYSTEMS; CLOSED LOOPS; CLOSED-LOOP DYNAMICS; FEEDBACKS]; GENERAL (CO); INPUT-TO-STATE (ISS) STABILITY; INPUT-TO-STATE-STABLE (ISS); LYAPUNOV; LYAPUNOV-KRASOVSKII FUNCTIONALS (LKF); NON LINEAR CONTROL;

AEROSPACE ENGINEERING; CLOSED LOOP CONTROL SYSTEMS; CLOSED LOOP SYSTEMS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; DYNAMICS; FEEDBACK; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MILITARY DATA PROCESSING; NONLINEAR CONTROL SYSTEMS; NONLINEAR SYSTEMS; SOUNDING APPARATUS; SYSTEM STABILITY; TELECOMMUNICATION NETWORKS;

CONTROL SYSTEMS;

EID: 46449138990     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282837     Document Type: Conference Paper

References (16)

1. A. Fattouh, O. Sename, and J.-M. Dion, A LMI Approach to Robust Observer Design for Linear Time-Delay Systems, in Proc. 39th IEEE Conf. Decision Control, Sydney, Australia, 2000, pp. 1495-1500.
2. M. Jankovic, Control-Lyapunov-Razumikhin Functions and Robust Stabilization of Time Delay Systems, IEEE Trans. Automat. Control, vol. 46, no. 7, July 2001, pp. 1048-1060.
3. I. Karafyllis, Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations, Nonlinear Anal. Theory Methods Appl., vol. 64, issue 3, February 2006, pp. 590-617.
4. H. Khalil, Nonlinear Systems, Third Edition, Prentice-Hall, Upper Saddle River, NJ; 2002.
5. V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht; 1999.
6. F. Mazene and P. Bliman, Backstepping Design for Time-Delay Nonlinear Systems, IEEE Trans. Automat. Control, vol. 51, no. 1, January 2006, pp. 149-154.
7. F. Mazene, M. Malisoff, and M. de Queiroz, Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems, Automatica, vol. 42, issue 10, October 2006, pp. 1663-1671.
8. F. Mazene, M. Malisoff, and Z. Lin, Further Results on Input-to-State Stability for Nonlinear Systems with Delayed Feedbacks, preprint available at http://www.math.lsu.edu/~malisoff/research.html.
9. W. Michiels, R. Sepulchre, D. Roose, and L. Moreau, A Perturbation Approach to the Stabilization of Nonlinear Cascade Systems with Time-Delay, in Proc. 42nd IEEE Conf. Decision Control, Las Vegas, NV, 2002, pp. 5782-5787.
10. ∞ Memoryless Control and an α-Stability Constraint for Time-Delay Systems; An LMI Approach, IEEE Trans. Automat. Control, vol. 43, no. 5, May 1998, pp. 739-743.
11. P. Pepe and Z.-P. Jiang, A Lyapunov-Krasovskii Methodology for ISS for Time-Delay Systems, in Proc. 44th IEEE Conf. Decision Control and European Control Conf., Seville, Spain, 2005, pp. 5782-5787.
12. E.D. Sontag, Smooth Stabilization Implies Coprime Factorization, IEEE Trans. Automat. Control, vol. 34, no. 4, April 1989, pp. 435-443.
13. E.D. Sontag, Input-to-State Stability: Basic Concepts and Results, in Nonlinear and Optimal Control Theory, P. Nistri and G. Stefani, eds., Springer Lecture Notes in Mathematics, Springer, Berlin, 2006, pp. 163-220.
14. E.D. Sontag and Y. Wang, On Characterizations of the Input-to-State Stability Property, Systems Control Lett., vol. 24, no. 5, 1995, pp. 351-359.
15. S. Tarbouriech and J. da Silva, Jr., Synthesis of Controllers for Continuous Time Delay Systems with Saturating Controls via LMI 's, IEEE Trans. Automat. Control, vol. 45, no. 1, January 2000, pp. 105-111.
16. A. Teel, Connections Between Razumikhin-Type Theorems and the ISS Nonlinear Small Gain Theorem, IEEE Trans. Automat. Control, vol. 43, no. 7, July 1998, pp. 960-964.