Mean square exponential stability of impulsive stochastic difference equations

Applied Mathematics Letters

Volumn 20, Issue 8, 2007, Pages 938-945

  Yang, Zhiguo ^a,b   Xu, Daoyi ^b  

^a SICHUAN NORMAL UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Difference equations; Difference inequality; Impulsive; Mean square exponential stability; Stochastic

Indexed keywords

ASYMPTOTIC STABILITY; RANDOM PROCESSES; STATISTICAL METHODS;

DIFFERENCE INEQUALITY; MEAN SQUARE EXPONENTIAL STABILITY; STOCHASTIC DIFFERENCE EQUATIONS;

DIFFERENCE EQUATIONS;

EID: 34047175867     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.09.006     Document Type: Article

References (19)

1. Kolmanovskii V.B., and Shaikhet L.E. Control of systems with aftereffect. Translations of Mathematical Monographs vol. 157 (1996), American Mathematical Society, Providence, RI
2. Kuchkina N., and Shaikhet L. Optimal control of Volterra type stochastic difference equations. Comput. and Math. Appl. 36 10-12 (1998) 251-259
3. Taniguchi T. Stability theorems of stochastic difference equations. J. Math. Anal. Appl. 147 1 (1990) 81-96
4. Ma F., and Caughey T.K. Mean stability of stochastic difference systems. Internat. J. Non-Linear Mech. 17 2 (1982) 69-84
5. Ma F., and Caughey T.K. Moment stability of linear stochastic difference systems. Mech. Res. Comm. 8 3 (1981) 143-151
6. Ahmadi G. On the mean square stability of linear difference equations. Appl. Math. Comput. 5 3 (1979) 233-241
7. Shaikhet L.E. Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations. Appl. Math. Lett. 10 3 (1997) 111-115
8. Kolmanovskii V., and Shaikhet L. Construction of Lyapunov functionals for stochastic hereditary systems: A survey of some recent results. Math. Comput. Modelling 36 6 (2002) 691-716
9. Kolmanovskii V., and Shaikhet L. Some peculiarities of the general method of Lyapunov functionals construction. Appl. Math. Lett. 15 (2002) 355-360
10. Zhang Q.Q. On a linear delay difference equation with impulses. Ann. Differential Equations 18 2 (2002) 197-204
11. Braverman E. On a discrete model of population dynamics with impulsive harvesting or recruitment. Nonlinear Anal. 63 5-7 (2005) 751-759
12. Wei G.P. The persistence of nonoscillatory solutions of difference equations under impulsive perturbations. Comput. and Math. Appl. 50 10-12 (2005) 1579-1586
13. Peng M.S. Oscillation theorems of second-order nonlinear neutral delay difference equations with impulses. Comput. and Math. Appl. 44 (2002) 741-748
14. Peng M.S. Oscillation criteria for second-order impulsive delay difference equations. Appl. Math. Comput. 146 1 (2003) 227-235
15. He Z.M., and Zhang X.M. Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions. Appl. Math. Comput. 156 (2004) 605-620
16. Xu D.Y., Ma Z., and Guo Q. Difference inequality and attraction domain of discrete-time systems. Ann. of Math. 20 A(1) (1999) 21-26 (in Chinese)
17. Pczkowska-Przdka K. Difference inequalities generated by impulsive parabolic differential-functional problems. J. Comput. Appl. Math. 84 2 (1997) 189-206
18. Hardy G., Littlewood J.E., and Pólya G. Inequalities. second ed. (1952), Cambridge University Press, New York
19. Liz E., and Ferreiro J.B. A note on the global stability of generalized difference equations. Appl. Math. Lett. 15 (2002) 655-659