Previous |  Up |  Next


moving invariant set; stability theory; uncertain impulsive differential-difference system
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.
[1] Bainov, D., Kostadinov, S., Nguyen, Van Min: Dichotomies and Integral Manifolds of Impulsive Differential Equations. SCT Publishing, Singapore (1994).
[2] Bainov, D., Stamova, I. M.: Vector Lyapunov functions and conditional stability for systems of impulsive differential-difference equations. ANZIAM J. 42 (2001), 341-353. DOI 10.1017/S1446181100011986 | MR 1818254 | Zbl 0980.93074
[3] Bainov, D., Dishliev, A. B., Stamova, I. M.: Continuous dependence of solutions of impulsive systems of differential-diference equations on initial data and on parameter. Bol. Soc. Parana. Mat. 18 (1998), 21-34. MR 1769790
[4] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Stability Analysis of Nonlinear Systems. Marcel Dekker, New York (1989). MR 0984861 | Zbl 0676.34003
[5] Lakshmikantham, V., Leela, S., Martynyuk, A. A.: Practical Stability of Nonlinear Systems. World Scientific Publishing, Singapore (1990). MR 1089428 | Zbl 0753.34037
[6] Lakshmikantham, V., Vatsala, S. A.: Stability of moving invariant sets. Advances in Nonlinear Dynamics. Langhorne, PA: Cordon and Breach. Stab. Control Theory Methods Appl. {\it 5} (1997), 79-83 Sivasundaram, S. MR 1479421 | Zbl 0947.34039
[7] Shendge, G. R.: A new approach to the stability theory of functional differential equations. J. Math. Anal. Appl. 95 (1983), 319-334. DOI 10.1016/0022-247X(83)90110-5 | MR 0716086
[8] Siljak, D. D., Ikeda, M., Ohta, Y.: Parametic stability. Proccedings Universita di Genova-Ohio State University Joint Conference: Birkhauser (1991), 1-20. MR 1125087
[9] Stamov, G.: Stability of moving invariant maniolds for impulsive differential equations. J. Tech. Univ. Plovdiv Fundam. Sci. Appl., Ser. A Pure Appl. Math. 7 (1999), 99-107. MR 1834207
[10] Stamov, G.: Stability of moving conditionally manifolds for impulsive differential equations. Adv. Stud. Contemp. Math. (Kyungshang) 9 (2004), 99-107. MR 2067833
[11] Stamov, G.: Impulsive integro-differential equations and stability of moving invariant maniolds. Methods Appl. Anal. 14 (2007), 69-76. MR 2392627
[12] Stamova, I., Stamov, G.: Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics. J. Comput. Appl. Math. 130 (2001), 163-171. DOI 10.1016/S0377-0427(99)00385-4 | MR 1827978 | Zbl 1022.34070
[13] Vatsala, A. S., Deo, G. S.: Stability of moving invariant sets for functional differential systems. Int. J. Nonlin. Diff. Eq.: Theory, Methods and Appl. 3 (1997), 179-186.
Partner of
EuDML logo