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SCIENCE CHINA Information Sciences, Volume 62 , Issue 7 : 072201(2019) https://doi.org/10.1007/s11432-018-9600-3

Aperiodically intermittent stochastic stabilization via discrete time or delay feedback control

Lei LIU 1,2, Matja$\check{\rm~z}$ PERC 3, Jinde CAO 1,*
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  • ReceivedApr 26, 2018
  • AcceptedSep 5, 2018
  • PublishedJun 5, 2019
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Abstract


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61304070, 61773152), the Chinese Postdoctoral Science Foundation (Grant Nos. 2016M601698, 2017T100318), the Jiangsu Province Postdoctoral Science Foundation (Grant No. 1701078B), and the Project Funded by the Qing Lan Project of Jiangsu Province, China.


References

[1] Khasminskii R. Stochastic Stability of Differential Equations. Alphen aan den Rijn: Sijthoff and Noordhoff, 1981. Google Scholar

[2] Boulanger C. Stabilization of a class of nonlinear stochastic systems. NOnlinear Anal-Theor Methods Appl, 2000, 41: 277-286 CrossRef Google Scholar

[3] Ma L F, Wang Z D, Han Q L. Consensus control of stochastic multi-agent systems: a survey. Sci China Inf Sci, 2017, 60: 120201 CrossRef Google Scholar

[4] Ma L F, Wang Z D, Liu Y R. A note on guaranteed cost control for nonlinear stochastic systems with input saturation and mixed time-delays. Int J Robust NOnlinear Control, 2017, 27: 4443-4456 CrossRef Google Scholar

[5] Arnold L, Crauel H, Wihstutz V. Stabilization of Linear Systems by Noise. SIAM J Control Optim, 1983, 21: 451-461 CrossRef Google Scholar

[6] Mao X R. Stochastic stabilization and destabilization. Syst Control Lett, 1994, 23: 279-290 CrossRef Google Scholar

[7] Appleby J A D, Mao X R, Rodkina A. Stabilization and Destabilization of Nonlinear Differential Equations by Noise. IEEE Trans Automat Contr, 2008, 53: 683-691 CrossRef Google Scholar

[8] Mao X R, Yin G G, Yuan C G. Stabilization and destabilization of hybrid systems of stochastic differential equations. Automatica, 2007, 43: 264-273 CrossRef Google Scholar

[9] Appleby J A D, Mao X R. Stochastic stabilisation of functional differential equations. Syst Control Lett, 2005, 54: 1069-1081 CrossRef Google Scholar

[10] Mao X R, Marion G, Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Processes their Appl, 2002, 97: 95-110 CrossRef Google Scholar

[11] Liu L, Shen Y. Noise suppresses explosive solutions of differential systems with coefficients satisfying the polynomial growth condition. Automatica, 2012, 48: 619-624 CrossRef Google Scholar

[12] Wu F K, Hu S G. Suppression and stabilisation of noise. Int J Control, 2009, 82: 2150-2157 CrossRef Google Scholar

[13] Cao J D, Li H X, Ho D W C. Synchronization criteria of Lur'e systems with time-delay feedback control. Chaos Solitons Fractals, 2005, 23: 1285-1298 CrossRef Google Scholar

[14] Chen W M, Xu S Y, Zou Y. Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control. Syst Control Lett, 2016, 88: 1-13 CrossRef Google Scholar

[15] Liu X Y, Ho D W C, Cao J D. Discontinuous Observers Design for Finite-Time Consensus of Multiagent Systems With External Disturbances.. IEEE Trans Neural Netw Learning Syst, 2017, 28: 2826-2830 CrossRef PubMed Google Scholar

[16] Mao X R, Lam J, Huang L R. Stabilisation of hybrid stochastic differential equations by delay feedback control. Syst Control Lett, 2008, 57: 927-935 CrossRef Google Scholar

[17] Sun J T. Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control. Chaos Solitons Fractals, 2004, 21: 143-150 CrossRef ADS Google Scholar

[18] Zhao H Y, Xie W. Hopf bifurcation for a small-world network model with parameters delay feedback control. NOnlinear Dyn, 2011, 63: 345-357 CrossRef Google Scholar

[19] Zhu Q X, Zhang Q Y. pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay. IET Control Theor Appl, 2017, 11: 1992-2003 CrossRef Google Scholar

[20] Dong R, Mao X R. Pth moment stabilization of hybrid systems by discrete-time feedback control. Stochastic Anal Appl, 2017, 35: 803-822 CrossRef Google Scholar

[21] Mao X R, Liu W, Hu L J. Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations. Syst Control Lett, 2014, 73: 88-95 CrossRef Google Scholar

[22] Song G F, Zheng B C, Luo Q. Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode. IET Control Theor Appl, 2017, 11: 301-307 CrossRef Google Scholar

[23] Song G F, Lu Z Y, Zheng B C. 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 CrossRef Google Scholar

[24] You S R, Liu W, Lu J Q. Stabilization of Hybrid Systems by Feedback Control Based on Discrete-Time State Observations. SIAM J Control Optim, 2015, 53: 905-925 CrossRef Google Scholar

[25] Guo Q, Mao X R, Yue R X. Almost sure exponential stability of stochastic differential delay equations. SIAM J Control Opt, 2016, 54: 1919-1933 CrossRef Google Scholar

[26] Mao X R. Almost Sure Exponential Stabilization by Discrete-Time Stochastic Feedback Control. IEEE Trans Automat Contr, 2016, 61: 1619-1624 CrossRef Google Scholar

[27] Chen W H, Zhong J C, Zheng W X. Delay-independent stabilization of a class of time-delay systems via periodically intermittent control. Automatica, 2016, 71: 89-97 CrossRef Google Scholar

[28] Gan Q T. Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control. Neural Process Lett, 2013, 37: 393-410 CrossRef Google Scholar

[29] Gan Q T, Zhang H, Dong J. Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control. Nonlin Anal-Model Contr, 2014, 19: 1--25. Google Scholar

[30] Liu Y, Jiang H J. Exponential stability of genetic regulatory networks with mixed delays by periodically intermittent control. Neural Comput Applic, 2012, 21: 1263-1269 CrossRef Google Scholar

[31] Li N, Cao J D. Intermittent control on switched networks via ${\varvec{\omega~}}$ ω -matrix measure method. NOnlinear Dyn, 2014, 77: 1363-1375 CrossRef Google Scholar

[32] Li C D, Feng G, Liao X F. Stabilization of Nonlinear Systems via Periodically Intermittent Control. IEEE Trans Circuits Syst II, 2007, 54: 1019-1023 CrossRef Google Scholar

[33] Mei J, Jiang M H, Wang B. Exponential $p$ p -Synchronization of Non-autonomous Cohen-Grossberg Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control. Neural Process Lett, 2014, 40: 103-126 CrossRef Google Scholar

[34] Wan Y, Cao J D. Distributed robust stabilization of linear multi-agent systems with intermittent control. J Franklin Institute, 2015, 352: 4515-4527 CrossRef Google Scholar

[35] Yang S J, Li C D, Huang T W. Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control.. Neural Networks, 2016, 75: 162-172 CrossRef PubMed Google Scholar

[36] Zhang G D, Shen Y. Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control.. IEEE Trans Neural Netw Learning Syst, 2015, 26: 1431-1441 CrossRef PubMed Google Scholar

[37] Zhang W, Li C D, Huang T W. Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput Applic, 2015, 26: 1781-1787 CrossRef Google Scholar

[38] Liu X W, Chen T P. Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control.. IEEE Trans Neural Netw Learning Syst, 2015, 26: 2396-2407 CrossRef PubMed Google Scholar

[39] Mao X R. Stochastic Differential Equations and Their Applications. Chichester: Horwood, 1997. Google Scholar