Delay-dependent stability of highly nonlinear neutral stochastic functional differential equations
Mingxuan Shen
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Search for more papers by this authorChen Fei
Business School, University of Shanghai for Science and Technology, Shanghai, China
Search for more papers by this authorCorresponding Author
Weiyin Fei
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Correspondence
Weiyin Fei, School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, Anhui 241000, China.
Email: [email protected]
Search for more papers by this authorXuerong Mao
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK
Search for more papers by this authorChunhui Mei
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Search for more papers by this authorMingxuan Shen
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Search for more papers by this authorChen Fei
Business School, University of Shanghai for Science and Technology, Shanghai, China
Search for more papers by this authorCorresponding Author
Weiyin Fei
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Correspondence
Weiyin Fei, School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, Anhui 241000, China.
Email: [email protected]
Search for more papers by this authorXuerong Mao
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK
Search for more papers by this authorChunhui Mei
Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, China
School of Mathematics, Physics and Finance, Anhui Polytechnic University, Wuhu, China
Search for more papers by this authorFunding information: National Natural Science Foundation of China, Grant/Award Numbers: 12271003; 62273003; Natural Science Foundation of University of Anhui, Grant/Award Numbers: KJ2020A0367; KJ2019A0141; Startup Foundation for Introduction Talent of AHPU, Grant/Award Numbers: 2020YQQ066; 2021YQQ058
Abstract
This article focuses on the delay-dependent stability of highly nonlinear hybrid neutral stochastic functional differential equations (NSFDEs). The delay dependent stability criteria for a class of highly nonlinear hybrid NSFDEs are derived via the Lyapunov functional. The stabilities discussed in this article include stability, asymptotically stability and exponential stability. A numerical example is given to illustrate the criteria established.
CONFLICT OF INTEREST
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.
Open Research
DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
REFERENCES
- 1Fei C, Fei W, Mao X, et al. Stabilisation of highly nonlinear hybrid systems by feedback control based on discrete-time state observations. IEEE Trans Automat Contr. 2020; 65(7): 2899-2912.
- 2Fei C, Fei W, Mao X, et al. Stability analysis of highly nonlinear hybrid multiple-delay stochastic differential equations. J Appl Anal Comput. 2019; 9: 1053-1070.
- 3Fei W, Hu L, Mao X, et al. Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems. Int J Robust Nonlin. 2019; 29: 1201-1215.
- 4Guo Q, Mao X, Yue R. Almost sure exponential stability of stochastic differential delay equations. SIAM J Control Optim. 2016; 54(4): 1919-1933.
- 5Mao X, Yuan C. Stochastic Differential Equations with Markovian Switching. Imperial College Press; 2006.
10.1142/p473 Google Scholar
- 6Song J, Niu Y, Zou Y. Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities. Automatica. 2018; 93: 33-41.
- 7Wang B, Zhu Q. Stability analysis of semi-Markov switched stochastic systems. Automatica. 2018; 94: 72-80.
- 8You S, Liu W, Lu J, et al. Stabilization of hybrid systems by feedback control based on discrete-time state observations. SIAM J Control Optim. 2015; 53(2): 905-925.
- 9Zhu Q, Cao J. th moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching. Nonlinear Dyn. 2012; 67: 829-845.
- 10Cao Y, Lam J, Hu L. Delay-dependent stochastic stability and analysis for time-delay systems with Markovian jumping parameters. J Frankl Inst. 2004; 340(6): 423-434.
- 11Li X, Cao J. Delay-independent exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms. Nonlinear Dyn. 2007; 50: 363-371.
- 12Mao X. Stochastic Differential Equations and Applications. 2nd ed. Horwood Publishing; 2007.
- 13Song G, Lu Z, Zheng B, et al. Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state. Sci China Inf Sci. 2018; 61:070213.
- 14Yan Z, Song Y, Park JH. Finite-time stability and stabilization for stochastic Markov jump systems with mode-dependent time delays. ISA Trans. 2017; 68: 141-149.
- 15Wu X, Tang Y, Cao J, et al. Stability analysis for continuous-time switched systems with stochastic switching signals. IEEE Trans Automat Contr. 2018; 63: 3083-3094.
- 16Wu X, Tang Y, Cao J. Input-to-state stability of time-varying switched systems with time delays. IEEE Trans Automat Contr. 2019; 64: 2537-2544.
- 17Hu L, Mao X, Zhang L. Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations. IEEE Trans Automat Contr. 2013; 59: 2319-2332.
- 18Fei W, Hu L, Mao X, et al. Structured robust stability and boundedness of nonlinear hybrid delay systems. SIAM J Control Optim. 2018; 56: 2662-2689.
- 19Wu F, Hu S. Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations. Int J Robust Nonlin. 2012; 22: 763-777.
- 20Wang Y, Wu F, Mao X. Stability in distribution of stochastic functional differential equations. Syst Control Lett. 2019; 132:104513.
- 21Li M, Mo H, Deng F. Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability. Appl Math Comput. 2019; 353: 320-328.
- 22Chen H, Shi P, Lim C, et al. Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications. IEEE Trans Cybern. 2016; 46: 1350-1362.
- 23Deng F, Mao W, Wang A. A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems. Appl Math Comput. 2013; 221: 132-143.
- 24Li M, Deng F. Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with Lévy noise. Nonlinear Anal Hybrid Syst. 2017; 24: 171-185.
- 25Luo Q, Mao X, Shen Y. New criteria on exponential stability of neutral stochastic differential delay equations. Syst Control Lett. 2006; 55: 826-834.
- 26Mao X, Shen Y, Yuan C. Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stoch Process Appl. 2008; 118: 1385-1406.
- 27Mo H, Li M, Deng F, et al. Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Sci China Inf Sci. 2018; 61:070214.
- 28Obradović M, Milošević M. Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method. J Comput Appl Math. 2017; 309: 244-266.
- 29Shen M, Fei C, Fei W, et al. Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays. Sci China Inf Sci. 2019; 62:202205.
- 30Shen M, Fei C, Fei W, et al. Stabilisation by delay feedback control for highly nonlinear neutral stochastic differential equations. Syst Control Lett. 2020; 137:104645.
- 31Shen M, Fei W, Mao X, et al. Exponential stability of highly nonlinear neutral pantograph stochastic differential equations. Asian J Control. 2020; 22: 436-448.
- 32Ngoc PHA. On exponential stability in mean square of neutral stochastic functional differential equations. Syst Control Lett. 2021; 154:104965.
- 33Wu F, Hu S, Huang C. Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. Syst Control Lett. 2010; 59: 195-202.
- 34Song Y, Shen Y. New criteria on asymptotic behavior of neutral stochastic functional differential equations. Automatica. 2013; 49: 626-632.
- 35Fei W, Hu L, Mao X, et al. Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica. 2017; 82: 165-170.
- 36Fei C, Shen M, Fei W, et al. Stability of highly nonlinear hybrid stochastic integro-differential delay equations. Nonlinear Anal Hybrid Syst. 2019; 31: 180-199.
- 37Song R, Wang B, Zhu Q. Delay-dependent stability of non-linear hybrid stochastic functional differential equations. IET Control Theory A. 2020; 14: 198-206.
- 38Shen M, Fei W, Mao X, et al. Stability of highly nonlinear neutral stochastic differential delay equations. Syst Control Lett. 2018; 115: 1-8.
- 39Kolmanovskii V, Koroleva N, Maizenberg T, et al. Neutral stochastic differential delay equations with Markovian switching. Stoch Anal Appl. 2003; 21: 819-847.
- 40Li X, Mao X, Yin G. 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: 847-892.
