Novel criteria for exponential stability in mean square of stochastic functional differential equations
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Abstract:
We present a novel approach to the mean square exponential stability of stochastic functional differential equations (SFDEqs). Consequently, new explicit criteria for the mean square exponential stability of SFDEqs are derived. Illustrative examples are provided.References
- E. Allen, Modeling with Itô stochastic differential equations, Mathematical Modelling: Theory and Applications, vol. 22, Springer, Dordrecht, 2007. MR 2292765
- Abraham Berman and Robert J. Plemmons, Nonnegative matrices in the mathematical sciences, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 544666
- Mou-Hsiung Chang, On Razumikhin-type stability conditions for stochastic functional differential equations, Math. Modelling 5 (1984), no. 5, 299–307. MR 781651, DOI 10.1016/0270-0255(84)90007-1
- Dehao Ruan, Liping Xu, and Jiaowan Luo, Stability of hybrid stochastic functional differential equations, Appl. Math. Comput. 346 (2019), 832–841. MR 3880069, DOI 10.1016/j.amc.2018.03.064
- Emilia Fridman and Leonid Shaikhet, Simple LMIs for stability of stochastic systems with delay term given by Stieltjes integral or with stabilizing delay, Systems Control Lett. 124 (2019), 83–91. MR 3899077, DOI 10.1016/j.sysconle.2018.12.007
- Yingxin Guo and Luyao Xin, Asymptotic and robust mean square stability analysis of impulsive high-order BAM neural networks with time-varying delays, Circuits Systems Signal Process. 37 (2018), no. 7, 2805–2823. MR 3812889, DOI 10.1007/s00034-017-0706-3
- Jinzhi Lei and Michael C. Mackey, Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system, SIAM J. Appl. Math. 67 (2006/07), no. 2, 387–407. MR 2285869, DOI 10.1137/060650234
- Qiang Li, Qi-min Zhang, and Bo-qiang Cao, Mean-square stability of stochastic age-dependent delay population systems with jumps, Acta Math. Appl. Sin. Engl. Ser. 34 (2018), no. 1, 145–154. MR 3772931, DOI 10.1007/s10255-018-0732-3
- Qi Luo, Xuerong Mao, and Yi Shen, Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations, Automatica J. IFAC 47 (2011), no. 9, 2075–2081. MR 2886823, DOI 10.1016/j.automatica.2011.06.014
- X. Mao, Stochastic differential equations and applications, Elsevier, New York, 2007.
- Pham Huu Anh Ngoc, Explicit criteria for mean square exponential stability of stochastic differential equations, Appl. Math. Lett. 93 (2019), 22–28. MR 3910841, DOI 10.1016/j.aml.2019.01.014
- Leonid Shaikhet, Lyapunov functionals and stability of stochastic functional differential equations, Springer, Cham, 2013. MR 3076210, DOI 10.1007/978-3-319-00101-2
- J. Michael Steele, Stochastic calculus and financial applications, Applications of Mathematics (New York), vol. 45, Springer-Verlag, New York, 2001. MR 1783083, DOI 10.1007/978-1-4684-9305-4
- Zhiguo Yan, Yunxia Song, and Ju H. Park, Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching, J. Franklin Inst. 355 (2018), no. 8, 3438–3454. MR 3788482, DOI 10.1016/j.jfranklin.2018.02.026
- Fuke Wu and Shigeng Hu, Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations, Internat. J. Robust Nonlinear Control 22 (2012), no. 7, 763–777. MR 2908915, DOI 10.1002/rnc.1726
- Bin Zhou and Weiwei Luo, Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems, Automatica J. IFAC 89 (2018), 382–391. MR 3762068, DOI 10.1016/j.automatica.2017.12.015
- Wuneng Zhou, Jun Yang, Xueqing Yang, Anding Dai, Huashan Liu, and Jian’an Fang, $p$th moment exponential stability of stochastic delayed hybrid systems with Lévy noise, Appl. Math. Model. 39 (2015), no. 18, 5650–5658. MR 3376096, DOI 10.1016/j.apm.2015.01.025
Additional Information
- Pham Huu Anh Ngoc
- Affiliation: Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Thu Duc District, Saigon, Vietnam
- Email: phangoc@hcmiu.edu.vn
- Received by editor(s): June 5, 2019
- Received by editor(s) in revised form: December 19, 2019
- Published electronically: March 25, 2020
- Additional Notes: The author was supported by the Vietnam National Foundation for Science and Technology Development under Grant 101.01-2019.04
- Communicated by: Wenxian Shen
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3427-3436
- MSC (2010): Primary 34D20, 93E15
- DOI: https://doi.org/10.1090/proc/14994
- MathSciNet review: 4108849