Cone-valued Lyapunov functions and stability for impulsive functional differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 7, 2008, Pages 2184-2191

  Liu, Kaien ^a   Yang, Guowei ^a  

^a QINGDAO UNIVERSITY   (China)

Author keywords

(Q0, Q) stability; Cone valued Lyapunov functions; Impulsive functional differential equations; Razumikhin technique; Stability in terms of two measures

Indexed keywords

BESSEL FUNCTIONS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); EXTRAPOLATION; FUNCTION EVALUATION; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MORPHOLOGY; SYSTEM STABILITY; TELECOMMUNICATION NETWORKS;

(MIN ,MAX ,+) FUNCTIONS; FUNCTIONAL DIFFERENTIAL EQUATIONS; LYAPUNOV;

STABILITY CRITERIA;

EID: 45349105537     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.07.057     Document Type: Article

References (11)

1. 0-stability of comparison differential systems. J. Math. Anal. Appl. 164 (1992) 307-324
2. 0-stability of comparison impulsive differential systems. Nonlinear Stud. 10 3 (2003) 247-257
3. Koksal S., and Lakshmikantham V. Higher derivatives of Lyapunov functions and cone-valued Lyapunov functions. Nonlinear Anal. 26 9 (1996) 1555-1564
4. Liu K.E., and Fu X.L. Stability of functional differential equations with impulses. J. Math. Anal. Appl. 328 (2007) 830-841
5. K.E. Liu, G.W. Yang, Stability and boundedness for impulsive functional differential equations, in: Proceedings of the 4th International Conference on Impulsive and Hybrid Dynamical Systems, 2007, pp. 42-46
6. Lakshmikantham V., and Leela S. Differential and Integral Inequalities vol. I (1969), Academic Press, New York
7. Lakshmikantham V., and Leela S. Cone-valued Lyapunov functions. Nonlinear Anal. 1 3 (1977) 215-222
8. Lakshmikantham V., and Liu X.Z. Stability Theory in Terms of Two Measures (1993), World Scientific, Singapore
9. Lakshmikantham V., Matrosov V.M., and Sivasundaram S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems (1991), Kluwer Academic Publishers, The Netherlands
10. Lakshmikantham V., and Papageorgiou N.S. Cone-valued Lyapunov functions and stability theory. Nonlinear Anal. 22 3 (1994) 381-390
11. Soliman A.A. On cone perturbing Lyapunov function for impulsive differential systems. Appl. Math. Comput. 163 (2005) 1069-1079