Mean square stability for controlled hybrid neutral stochastic differential equations with infinite delay. (English) Zbl 1534.93476
MSC:
| 93E15 | Stochastic stability in control theory |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
controlled hybrid neutral stochastic differential equations; infinite delay; mean square stability; existence and uniqueness of solutionReferences:
| [1] | AgarwalP, AgarwalRP, RuzhanskyM. Special Functions and Analysis of Differential Equations. Chapman and Hall/CRC; 2020. |
| [2] | El‐SayedAA, AgarwalP. Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials. Math Methods Appl Sci. 2019;42(11):3978‐3991. · Zbl 1425.65124 |
| [3] | ErturkVS, GodweE, BaleanuD, KumarP, AsadJ, JajarmiA. Novel fractional‐order Lagrangian to describe motion of beam on nanowire. Acta Phys Pol A. 2021;140(3):265‐272. |
| [4] | GençoğluMT, AgarwalP. Use of quantum differential equations in sonic processes. Appl Math Nonlinear Sci. 2021;6(1):21‐28. · Zbl 1524.81025 |
| [5] | JajarmiA, BaleanuD, VahidKZ, MobayenS. A general fractional formulation and tracking control for immunogenic tumor dynamics. Math Methods Appl Sci. 2022;45(2):667‐680. · Zbl 1531.92026 |
| [6] | ZhangX, AgarwalP, LiuZ, PengH. The general solution for impulsive differential equations with Riemann‐Liouville fractional‐order [( q\in \left(1,2\right) \]\). Open Math. 2015;13:908‐923. · Zbl 1350.34017 |
| [7] | ZhangW, SongMH, LiuMZ. Strong convergence of the truncated Euler-Maruyama method for stochastic functional differential equations. Int J Comput Math. 2017;95(12):2363‐2387. · Zbl 1499.65299 |
| [8] | ZhangX, AgarwalP, LiuZ, PengH, YouF, ZhuY. Existence and uniqueness of solutions for stochastic differential equations of fractional‐order [( q>1 \]\) with finite delays. Adv Differ Equ. 2017;2017:123. · Zbl 1422.34083 |
| [9] | HuY, WuF, HuangC. Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay. Automatica. 2009;45:2577‐2584. · Zbl 1368.93765 |
| [10] | LiX, FuX. Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks. J Comput Appl Math. 2010;234:407‐417. · Zbl 1193.34168 |
| [11] | LiX, MaoX, YinG. Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability. IMA J Numer Anal. 2019;39(2):847‐892. · Zbl 1461.65007 |
| [12] | LiuL, DengF, HouT. Almost sure exponential stability of implicit numerical solution for stochastic functional differential equation with extended polynomial growth condition. Appl Math Comput. 2018;330:201‐212. · Zbl 1427.60108 |
| [13] | MaoX. Robustness of exponential stability of stochastic differential delay equations. IEEE Trans Automat Contr. 1996;41:442‐447. · Zbl 0851.93074 |
| [14] | MaoX. Stochastic Differential Equations and Applications. Ellis; 1997. · Zbl 0892.60057 |
| [15] | MaoX. Exponential Stability of Stochastic Differential Equations. Marcel Dekker; 1994. · Zbl 0806.60044 |
| [16] | Pavlovic̀G, JankovićS. Razumikhin‐type theorems on general decay stability of stochastic functional differential equations with infinite delay. J Comput Appl Math. 2012;236:1679‐1690. · Zbl 1247.34128 |
| [17] | RenY, LuS, XiaN. Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay. J Comput Appl Math. 2008;220:364‐372. · Zbl 1152.34388 |
| [18] | ShenM, FeiC, FeiW, MaoX. Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays.Sci China Inf Sci. 2019;62:202205. |
| [19] | SongR, WangB, ZhuQ. Delay‐dependent stability of non‐linear hybrid stochastic functional differential equations. IET Control Theory Appl. 2020;14(2):198‐206. · Zbl 07907048 |
| [20] | SowmiyaC, RajaR, ZhuQ, RajchakitG. Further mean‐square asymptotic stability of impulsive discrete‐time stochastic BAM neural networks with Markovian jumping and multiple time‐varying delays. J Franklin Inst. 2019;356(1):561‐591. · Zbl 1405.93193 |
| [21] | WeiF, WangK. The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay. J Math Anal Appl. 2007;331(1):516‐531. · Zbl 1121.60064 |
| [22] | WuF, HuS. Razumikhin type theorems on general decay stability and robustness for stochastic functional differential equations. Int J Robust Nonlinear Control. 2012;22:763‐777. · Zbl 1276.93081 |
| [23] | HuL, MaoX, ShenY. Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Syst Control Lett. 2013;62:178‐187. · Zbl 1259.93127 |
| [24] | MaoX, YuanC. Stochastic Differential Equations with Markovian Switching. Imperial College Press; 2006. |
| [25] | MeiC, FeiC, FeiW, MaoX. Exponential stabilization by delay feedback control for highly nonlinear hybrid stochastic functional differential equations with infinite delay. Nonlinear Anal Hybrid Syst. 2021;40:101026. · Zbl 1483.93527 |
| [26] | MeiC, LiangY, FeiW, MaoX. Feedback delay control of highly nonlinear stochastic functional differential equations with discrete‐time state observations. Math Methods Appl Sci. 2021. doi:10.1002/mma.7718 |
| [27] | ChanthornP, RajchakitG, ThipchaJ, et al. Robust stability of complex‐valued stochastic neural networks with time‐varying delays and parameter uncertainties. Mathematics. 2020;8(5):742. |
| [28] | FeiW, HuL, MaoX, ShenM. Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica. 2017;82:165‐170. · Zbl 1376.93115 |
| [29] | FengL, LiS, MaoX. Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching. J Franklin Inst. 2016;353(18):4924‐4949. · Zbl 1349.93329 |
| [30] | CaraballoT, MchiriL, BelfekiM. [( \eta \]\)‐stability of hybrid neutral stochastic differential equations with infinite delay. Int J Robust Nonlinear Control. 2022;32:1973‐1989. doi:10.1002/rnc.5931 · Zbl 07769338 |
| [31] | WuA, YouS, MaoW, MaoX, HuL. On exponential stability of hybrid neutral stochastic differential delay equations with different structures. Nonlinear Anal Hybrid Syst. 2021;39:100971. · Zbl 1478.93563 |
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