# American Institute of Mathematical Sciences

• Previous Article
Some representations of moore-penrose inverse for the sum of two operators and the extension of the fill-fishkind formula
• NACO Home
• This Issue
• Next Article
Second order cone programming formulation of the fixed cost allocation in DEA based on Nash bargaining game
doi: 10.3934/naco.2021024
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies

 1 College of Liberal Arts and Sciences, National University of Defense Technology, Hunan, 410000, China 2 School of Mathematics and Statistics, Yulin Normal University, Guangxi 537000, China 3 College of Mathematics and Statistics, Guangxi Normal University, Guangxi, 537000, China

* Corresponding author: Jianhua Huang

Received  April 2021 Revised  June 2021 Early access June 2021

Fund Project: The first author is supported by the partial supports of the Natural Science Foundation of Guangxi Province (2018JJA110105), the Foundation of Yulin Normal University (G2019ZK12), Middle-aged and Young Teachers’ Basic Ability Promotion Project of Guangxi (2019KY0587), China.
The second author is supported by the partial supports of the Natural Science Foundation of Guangxi Province (2019AC20186), China.

We investigate the consensus stability for linear stochastic multi-agent systems with multiplicative noises and Markovian random graphs and investigate the asymptotic consensus in the mean square sense for the systems. To establish the consensus stability for the systems, we analysis the consensus error systems by developing general stochastic differential equation with jumps, matrix theory and algebraic graph theory, and then show that the error consensus in the mean square sense finally tending to zero as time goes on is determined by the strongly connected property of union of topologies. Finally, we provide an example to demonstrate the effectiveness of our theoretical results.

Citation: Xiaojin Huang, Hongfu Yang, Jianhua Huang. Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2021024
##### References:

show all references

##### References:
 [1] Hussain Alazki, Alexander Poznyak. Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method. Journal of Industrial & Management Optimization, 2016, 12 (1) : 169-186. doi: 10.3934/jimo.2016.12.169 [2] Boris P. Belinskiy, Peter Caithamer. Stochastic stability of some mechanical systems with a multiplicative white noise. Conference Publications, 2003, 2003 (Special) : 91-99. doi: 10.3934/proc.2003.2003.91 [3] Young-Pil Choi, Samir Salem. Cucker-Smale flocking particles with multiplicative noises: Stochastic mean-field limit and phase transition. Kinetic & Related Models, 2019, 12 (3) : 573-592. doi: 10.3934/krm.2019023 [4] Wenqiang Zhao. Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on $\mathbb{R}^N$ driven by multiplicative noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3453-3474. doi: 10.3934/dcdsb.2018251 [5] Xi Zhu, Meixia Li, Chunfa Li. Consensus in discrete-time multi-agent systems with uncertain topologies and random delays governed by a Markov chain. Discrete & Continuous Dynamical Systems - B, 2020, 25 (12) : 4535-4551. doi: 10.3934/dcdsb.2020111 [6] Tao Jiang, Xianming Liu, Jinqiao Duan. Approximation for random stable manifolds under multiplicative correlated noises. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3163-3174. doi: 10.3934/dcdsb.2016091 [7] Abiti Adili, Bixiang Wang. Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative noise. Conference Publications, 2013, 2013 (special) : 1-10. doi: 10.3934/proc.2013.2013.1 [8] Xiaoling Zou, Dejun Fan, Ke Wang. Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1507-1519. doi: 10.3934/dcdsb.2013.18.1507 [9] Junyi Tu, Yuncheng You. Random attractor of stochastic Brusselator system with multiplicative noise. Discrete & Continuous Dynamical Systems, 2016, 36 (5) : 2757-2779. doi: 10.3934/dcds.2016.36.2757 [10] T. Caraballo, M. J. Garrido-Atienza, J. López-de-la-Cruz. Dynamics of some stochastic chemostat models with multiplicative noise. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1893-1914. doi: 10.3934/cpaa.2017092 [11] Yicheng Liu, Yipeng Chen, Jun Wu, Xiao Wang. Periodic consensus in network systems with general distributed processing delays. Networks & Heterogeneous Media, 2021, 16 (1) : 139-153. doi: 10.3934/nhm.2021002 [12] Mario Roy, Mariusz Urbański. Random graph directed Markov systems. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 261-298. doi: 10.3934/dcds.2011.30.261 [13] Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete & Continuous Dynamical Systems, 2001, 7 (3) : 487-515. doi: 10.3934/dcds.2001.7.487 [14] Alexandra Rodkina, Henri Schurz, Leonid Shaikhet. Almost sure stability of some stochastic dynamical systems with memory. Discrete & Continuous Dynamical Systems, 2008, 21 (2) : 571-593. doi: 10.3934/dcds.2008.21.571 [15] Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021066 [16] H.Thomas Banks, Shuhua Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. Mathematical Biosciences & Engineering, 2012, 9 (1) : 1-25. doi: 10.3934/mbe.2012.9.1 [17] Felix X.-F. Ye, Yue Wang, Hong Qian. Stochastic dynamics: Markov chains and random transformations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2337-2361. doi: 10.3934/dcdsb.2016050 [18] Min Zhao, Shengfan Zhou. Random attractor for stochastic Boissonade system with time-dependent deterministic forces and white noises. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1683-1717. doi: 10.3934/dcdsb.2017081 [19] Jiahui Zhu, Zdzisław Brzeźniak. Nonlinear stochastic partial differential equations of hyperbolic type driven by Lévy-type noises. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3269-3299. doi: 10.3934/dcdsb.2016097 [20] Haiyan Zhang. A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1287-1301. doi: 10.3934/jimo.2016.12.1287