随机泛函微分方程的Lyapunov指数分析
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摘要
提出对随机泛函微分方程的Lyapunov指数分析。首先,提取随机泛函微分方程的Lyapunov指数函数,结合LMIs形式得到随机泛函微分方程的鲁棒指数原则,构建数值算例,以此验证鲁棒指数原则;其次,提出时滞分解方法,通过分析不同参数下的Lyapunov指数的时滞上界值,确定Lyapunov指数的性能,实现随机泛函微分方程的Lyapunov指数分析。实验证明,通过对随机泛函微分方程稳定性的描述有效地完成了Lyapunov指数分析,所提出的时滞分解法在不同参数下对随机泛函微分方程的Ly-apunov收敛效果较好。
The Lyapunov exponent analysis of stochastic functional differential equations is presented.First of all, Lyapunov exponential function of Stochastic Functional Differential Equations with LMIs extraction, the principle of robust exponential form of stochastic functional differential equations,constructing numerical examples to verify the robust exponential principle; secondly, the delay decomposition method, the upper bound analysis of Lyapunov index under different parameter values,determine the performance index of Lyapunov, Lyapunov index analysis of stochastic functional differential equations. The experiment proved that the stability of stochastic functional differential equations to describe the effective completion of the Lyapunov index analysis, the proposed delay decomposition method Lyapunov convergence effect of stochastic functional differential equations better under different parameters.
The Lyapunov exponent analysis of stochastic functional differential equations is presented.First of all, Lyapunov exponential function of Stochastic Functional Differential Equations with LMIs extraction, the principle of robust exponential form of stochastic functional differential equations,constructing numerical examples to verify the robust exponential principle; secondly, the delay decomposition method, the upper bound analysis of Lyapunov index under different parameter values,determine the performance index of Lyapunov, Lyapunov index analysis of stochastic functional differential equations. The experiment proved that the stability of stochastic functional differential equations to describe the effective completion of the Lyapunov index analysis, the proposed delay decomposition method Lyapunov convergence effect of stochastic functional differential equations better under different parameters.
引文
[1]洪涛,宋茂忠,王保云.基于随机天线阵的物理层安全通信系统峰均功率比问题研究[J].电子与信息学报,2015,37(1):188-192.
[2]陈华.一类具有随机扰动的谣言传播模型的动力学行为分析[J].科技通报,2016,32(6):139-144.
[3]李红星,陆安山,陆益民.鲁棒滤波在船舶横摇随机控制系统中的应用[J].西南大学学报(自然科学版),2016,38(6):153-158.
[4]蒋登辉,李艳.带乘性噪声的随机控制系统鲁棒H2/H∞控制设计[J].山东科技大学学报(自然科学版),2016,35(3):92-98.
[5]俞华军.带有非线性扰动的不确定时滞系统鲁棒预测控制[J].电子设计工程,2016,24(6):190-193.
[6]陈晓轩,刘志勇,李文娟.高阶非线性控制系统线性化镇定可行域分析[J].阜阳师范学院学报:自然科学版,2016,33(3):1-5.
[7]姚廷富,施妮沙,吴宗显,等.一类无限维Cartan型Lie代数的Witt子代数与模[J].贵州师范大学学报(自然版),2016,34(2):64-67.
[8]邢鹏超,姜健飞.张量与矩阵乘积的递推算法及相关问题[J].东华大学学报(自然科学版),2015,41(5):711-717.
[9]季晓蕾,王阳.切换广义系统的一类统一Lyapunov函数初探[J].沈阳化工大学学报,2015,29(4):368-370.
[10]李欢欢,姜偕富,唐超超.一类时变时滞系统的稳定性准则[J].杭州电子科技大学学报,2016,36(4):52-56.
[2]陈华.一类具有随机扰动的谣言传播模型的动力学行为分析[J].科技通报,2016,32(6):139-144.
[3]李红星,陆安山,陆益民.鲁棒滤波在船舶横摇随机控制系统中的应用[J].西南大学学报(自然科学版),2016,38(6):153-158.
[4]蒋登辉,李艳.带乘性噪声的随机控制系统鲁棒H2/H∞控制设计[J].山东科技大学学报(自然科学版),2016,35(3):92-98.
[5]俞华军.带有非线性扰动的不确定时滞系统鲁棒预测控制[J].电子设计工程,2016,24(6):190-193.
[6]陈晓轩,刘志勇,李文娟.高阶非线性控制系统线性化镇定可行域分析[J].阜阳师范学院学报:自然科学版,2016,33(3):1-5.
[7]姚廷富,施妮沙,吴宗显,等.一类无限维Cartan型Lie代数的Witt子代数与模[J].贵州师范大学学报(自然版),2016,34(2):64-67.
[8]邢鹏超,姜健飞.张量与矩阵乘积的递推算法及相关问题[J].东华大学学报(自然科学版),2015,41(5):711-717.
[9]季晓蕾,王阳.切换广义系统的一类统一Lyapunov函数初探[J].沈阳化工大学学报,2015,29(4):368-370.
[10]李欢欢,姜偕富,唐超超.一类时变时滞系统的稳定性准则[J].杭州电子科技大学学报,2016,36(4):52-56.