状态依赖时滞跳跃扩散系统的随机输入–状态稳定性分析
Stochastic Input-to-State Stability Analysis for State-Dependent Delayed Jump-Diffusion Systems
摘要: 随机系统在众多领域中有着广泛的应用，因此许多学者对随机系统进行了研究，其中稳定性是研究随机系统的核心内容。本文利用增量Lyapunov函数方法给出了状态依赖时滞跳跃扩散系统的随机输入–状态稳定性的充分条件，并基于该条件运用反证法与Markov不等式证明了状态依赖时滞跳跃扩散系统的随机稳定性，从而丰富了随机系统稳定性的研究结果。
Abstract: Stochastic systems have a wide range of applications in many fields, so many scholars have studied stochastic systems, of which stability is the core content of studying stochastic systems. In this pa-per, the incremental Lyapunov function method is used to give sufficient conditions for the sto-chastic input-to-state stability of the state-dependent delayed jump-diffusion systems, and based on this condition, the stochastic stability of the state-dependent delayed jump-diffusion systems is proved by using the contradictory method and Markov’s inequality, thereby enriching the results of the stochastic system stability.
文章引用：袁香凝, 韩金越, 高铱钒, 任院红. 状态依赖时滞跳跃扩散系统的随机输入–状态稳定性分析[J]. 理论数学, 2022, 12(11): 1918-1924. https://doi.org/10.12677/PM.2022.1211206

参考文献

[1] Zamani, M., Rungger, M. and Esfahani, P.M. (2017) Approximations of Stochastic Hybrid Systems: A Compositional Approach. IEEE Transactions on Automatic Control, 62, 2838-2853. [Google Scholar] [CrossRef] 
[2] Jagtap, P. and Zamani, M. (2018) Backstepping Design for In-cremental Stability of Stochastic Hamiltonian Systems with Jumps. IEEE Transactions on Automatic Control, 63, 255-261. [Google Scholar] [CrossRef] 
[3] Li, X. and Yang, X. (2020) Lyapunov Stability Analysis for Nonlinear Systems with State-Dependent State Delay. Automatica, 112, Article ID: 108674. [Google Scholar] [CrossRef] 
[4] Li, X. and Peng, D. (2022) Uniform Stability of Nonlinear Systems with State-Dependent Delay. Automatica, 137, Article ID: 110098. [Google Scholar] [CrossRef] 
[5] Bekiaris-Liberis, N. and Krstic, M. (2013) Compensation of State-Dependent Input Delay for Nonlinear Systems. IEEE Transactions on Automatic Control, 58, 275-289. [Google Scholar] [CrossRef] 
[6] Hamadeh, A., Stan, G.B. and Goncalves, J. (2012) Global State Synchronization in Networks of Cyclic Feedback Systems. IEEE Transactions on Automatic Control, 57, 478-483. [Google Scholar] [CrossRef] 
[7] Pola, G., Girard, A. and Tabuada, P. (2008) Approximately Bisimilar Symbolic Models for Nonlinear Control Systems. Automatica, 44, 2508-2516. [Google Scholar] [CrossRef] 
[8] Bond, B.N., Mahmood, Z., Li, Y., Sredojevic, R., Megretski, A., Stojanovi, V., Avniel, Y. and Daniel, L. (2010) Compact Modeling of Nonlinear Analog Circuits Using System Identification via Semidefinite Programming and Incremental Stability Certification. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 29, 1149-1162. [Google Scholar] [CrossRef] 
[9] Stan, G.B. and Sepulchre, R. (2007) Analysis of Interconnected Oscillators by Dissipativity Theory. IEEE Transactions on Automatic Control, 52, 256-270. [Google Scholar] [CrossRef] 
[10] Jagtap, P. and Zamani, M. (2020) Symbolic Models for Retarded Jump-Diffusion Systems. Automatica, 111, Article ID: 108666. [Google Scholar] [CrossRef] 
[11] Zamani, M., Wouw, N.V.D. and Majumdar, R. (2013) Backstepping Controller Synthesis and Characterizations of Incremental Stability. Systems & Control Letters, 62, 949-962. [Google Scholar] [CrossRef] 

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