The problem of the absolute continuity for Lyapunov-Krasovskii functionals

IEEE Transactions on Automatic Control

Volumn 52, Issue 5, 2007, Pages 953-957

  Pepe, Pierdomenico ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Functional differential equations; Input to state stability (ISS); Lyapunov Krasovskii theorem; Nonlinear time delay systems

Indexed keywords

DIFFERENCE EQUATIONS; INVARIANCE; LYAPUNOV FUNCTIONS; TIME DELAY;

FUNCTIONAL DIFFERENTIAL EQUATIONS; INPUT-TO-STATE STABILITY; LYAPUNOV-KRASOVSKII THEOREM; NONLINEAR TIME-DELAY SYSTEM;

NONLINEAR CONTROL SYSTEMS;

EID: 34249106681     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.895855     Document Type: Article

References (21)

1. D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of integral input to state stability," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1082-1097, Jun. 2000.
2. A. Bacciotti and L. Rosier, Lyapunov Functions and Stability in Control Theory, 2nd ed. Berlin, Germany: Springer-Verlag, 2005.
3. E.-K. Boukas and Z.-K. Liu, Deterministic and Stochastic Time Delay Systems. Boston, MA: Birkhäuser, 2002.
4. T. A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations. New York: Academic, 1985, vol. 178, Mathematics in Science and Engineering.
5. R. D. Driver, "Existence and stability of solutions of a delay-differential system," Arch. Rational Mech. Anal., no. 10, pp. 401-426, 1962.
6. L. Dugard and E. I. Verriest, Stability and Control of Time-Delay Systems. New York: Springer-Verlag, 1998, vol. 228, Lecture Notes in Control and Information Sciences.
7. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time Delay Systems Boston, MA: Birkhäuser, 2003.
8. J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
9. I. Karafyllis, "Lyapunov theorems for systems described by retarded functional differential equations," Nonlinear Anal.: Theory, Meth., Appl., vol. 64, no. 3, pp. 590-617, 2006.
10. V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations. Norwell, MA: Kluwer, 1999.
11. L. A. Lusternik and V. J. Sobolev, Elements of Functional Analysis New York: Wiley, 1974.
12. M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems New York: Marcel-Dekker, 2000.
13. S.-I. Niculescu, Delay Effects on Stability, a Robust Control Approach. New York: Springer-Verlag, 2001, Lecture Notes in Control and Information Sciences.
14. T. Oguchi, A. Watanabe, and T. Nakamizo, "Input-output linearization of retarded nonlinear systems by using an extension of lie derivative," Int. J. Control, vol. 75, no. 8, pp. 582-590, 2002.
15. P. Pepe and Z.-P. Jiang, "A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems," Syst. Control Lett., vol. 55, no. 12, pp. 1006-1014, 2006.
16. P. Pepe, "On Lyapunov-Krasovskii functionals under Carathéodory conditions," Automatica, vol. 43, no. 4, pp. 701-706, 2007.
17. N. Rouche, P. Habets, and M. Laloy, Stability Theory by Lyapunov's Direct Method. Berlin, Germany: Springer-Verlag, 1977.
18. H. L. Royden, Real Analysis, 3rd ed. New York: Macmillan, 1988.
19. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Autom. Control, vol. 34, no. 4, pp. 435-443, Apr. 1989.
20. A. R. Teel, "Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem," IEEE Trans. Autom. Control, vol. 43, no. 7, pp. 960-964, Jul. 1998.
21. T. Yoshizawa, Stability Theory by Lyapunov's Second Method. Tokyo, Japan: Math. Soc. Japan, 1966.