混杂随机系统基于离散时间状态观测的几乎必然指数镇定
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摘要
基于离散时间状态观测,研究混杂随机系统的几乎必然指数镇定.在扩散项和漂移项中同时加入反馈控制器,通过选取适当的Lyapunov函数,利用Markov链的平稳分布和稳定性分析的方法,得到混杂随机系统的几乎必然指数镇定,再通过含有线性反馈控制器系统的稳定性来说明所得结果的可行性.
The paper studies the almost surely exponential stabilization of hybrid stochastic systems,based on the observations of discrete-time state and the control function which is embedded into the drift part and diffusion part. We get the almost surely exponential stabilization of the hybrid random system by choosing appropriate Lyapunov function, using Markov chain stationary distribution and methods of stability analysis. The stability of the system with linear feedback controller is used to illustrate the feasibility of the results.
The paper studies the almost surely exponential stabilization of hybrid stochastic systems,based on the observations of discrete-time state and the control function which is embedded into the drift part and diffusion part. We get the almost surely exponential stabilization of the hybrid random system by choosing appropriate Lyapunov function, using Markov chain stationary distribution and methods of stability analysis. The stability of the system with linear feedback controller is used to illustrate the feasibility of the results.
引文
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[9]PENG S G,ZHANG Y,YU S M.Global mean-square exponential stabilization of stochastic system with time delay via impulsive control[J].Asian Journal of Control,2012,14(1):288-299.
[10]MAO X R.Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control[J].Automatica,2013,49(12):3677-3681.
[11]MAO X R,LIU W,HU L J,et al.Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations[J].Systems&Control Letters,2014,73:88-95.
[12]MAO X R,YIN G G,YUANC G.Stabilization and destabilization of hybrid systems of stochastic differential equations[J].Automatica,2007,43(2):264-273.
[13]DONG R.Almost sure exponential stabilization by stochastic feedback control based on discrete-time observations[J].Stochastic Analysis Applications,2018,36(4):561-583.
[14]SONG G F,LU Z Y,ZHENG B C,et al.Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state[J].Science China Information Sciences,2018,61(7):130-145.
[2]高远.混沌系统的参数微扰随机脉冲控制[J].广西工学院学报,2004,15(2):14-18.
[3]QIU Q W,LIU W,HU L J,et al.Stabilization of stochastic differential equations with markovian switching by feedback control based on discretetime state observation with a time delay[J].Statistics&Probability Letters,2016,115:16-26.
[4]YIN G,XI F B.Stability of regime-switching jump diffusions[J].SIAM journalon control and optimization,2010,48(7):4525-4549.
[5]ZHANG D F,CHEN Z J.Exponential stability for stochastic differential equation driven by G-Brownian motion[J].Applied Mathematics Letters,2012,25(11):1906-1910.
[6]DONG R,MAO X R.On pth moment stabilization of hybrid system sby discrete-time feedback control[J].Stochastic Analysis and Applications,2017,35(1):1-20.
[7]ZHU Q X,ZHANG Q Y.Pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discretetime state observations with a time delay[J].Iet Control Theory&Applications,2017,11(12):1992-2003.
[8]LI Y Y,LU J Q,MAO X R,et al.Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations[J].Asian Journal of Control,2017,19(2):1943-1953.
[9]PENG S G,ZHANG Y,YU S M.Global mean-square exponential stabilization of stochastic system with time delay via impulsive control[J].Asian Journal of Control,2012,14(1):288-299.
[10]MAO X R.Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control[J].Automatica,2013,49(12):3677-3681.
[11]MAO X R,LIU W,HU L J,et al.Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations[J].Systems&Control Letters,2014,73:88-95.
[12]MAO X R,YIN G G,YUANC G.Stabilization and destabilization of hybrid systems of stochastic differential equations[J].Automatica,2007,43(2):264-273.
[13]DONG R.Almost sure exponential stabilization by stochastic feedback control based on discrete-time observations[J].Stochastic Analysis Applications,2018,36(4):561-583.
[14]SONG G F,LU Z Y,ZHENG B C,et al.Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state[J].Science China Information Sciences,2018,61(7):130-145.