具有单个时滞的基因调控网络的稳定性分析
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摘要
为了减少具有时滞的基因调控网络在实际问题研究和应用中的保守性,对仅具有单个时滞(翻译时滞)的基因调控网络在均方根意义上的全局指数稳定性进行分析。将时滞假设为随机和时变的,且其概率分布是先验已知的。通过采用时滞的概率分布信息,利用辅助时滞参数的Lyapunov函数、稀疏矩阵和LMI技术,得出仅具有翻译时变时滞的确定性和不确定性的基因调控网络指数稳定性的判据。运用MATLAB中的LMI和Simulink 2个工具箱对实例进行仿真,结果验证了所提理论的正确性。
In order to reduce the conservativeness of the gene regulatory networks with time-delay in the research and application of practical problems,the global exponential stability in the mean square sense of gene regulatory networks with only a single delay(translation delay)was analyzed.The time delay was assumed to be random and time variant,and its probability distribution information was also assumed to be a priori.Under these kinds of assumptions,the criteria of exponential stability for certain and uncertain gene regulatory networks with translation time-varying delay was then made possible,where probability distribution information of the time delay,together with the Lyapunov function under auxiliary delay parameter,as well as the sparse matrix and LMI techniques,were collectively employed to do so.The correctness of the theory was illustrated by two simulated numerical examples through two tool boxes of LMI and Simulink in MATLAB.
In order to reduce the conservativeness of the gene regulatory networks with time-delay in the research and application of practical problems,the global exponential stability in the mean square sense of gene regulatory networks with only a single delay(translation delay)was analyzed.The time delay was assumed to be random and time variant,and its probability distribution information was also assumed to be a priori.Under these kinds of assumptions,the criteria of exponential stability for certain and uncertain gene regulatory networks with translation time-varying delay was then made possible,where probability distribution information of the time delay,together with the Lyapunov function under auxiliary delay parameter,as well as the sparse matrix and LMI techniques,were collectively employed to do so.The correctness of the theory was illustrated by two simulated numerical examples through two tool boxes of LMI and Simulink in MATLAB.
引文
[1] 扶凌云.基因调控网络鲁棒稳定性分析[D].长沙:中南大学,2011.FU L Y.Robust stability analysis of gene regulatory networks[D].Changsha:Central South University,2011.
[2] 王沛,吕金虎.基因调控网络的控制:机遇与挑战[J].自动化学报,2013,39(12):1969-1979.WANG P,LYU J H.Control of genetic regulatory networks:Opportunities and challenges[J].Acta Automatica Sinica,2013,39(12):1969-1979.
[3] 何勇,曾进,吴敏,等.具有区间时滞的离散时间基因调控网络稳定性研究[J].控制理论与应用,2012,29(11):1465-1470.HE Y,ZENG J,WU M,et al.Stability for discrete-time genetic regulatory networks with time-varying interval delays[J].Control Theory & Applications,2012,29(11):1465-1470.
[4] JIANG N,LIU X,YU W,et al.Finite-time stochastic synchronization of genetic regulatory networks[J].Neurocomputing,2015,167:314-321.
[5] WANG W,NGUANG S K,ZHONG S,et al.Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties[J].Communications in Nonlinear Science & Numerical Simulation,2014,19(5):1569-1581.
[6] LI C,CHEN L,AIHARA K.Synchronization of coupled nonidentical genetic oscillators[J].Physical Biology,2006,3(1):37-44.
[7] LOU X,YE Q,CUI B.Exponential stability of genetic regulatory networks with random delays[J].Neurocomputing,2010,73(4):759-769.
[8] ZHANG X,LI R,HAN C,et al.Robust stability analysis of uncertain genetic regulatory networks with mixed time delays[J].International Journal of Machine Learning & Cybernetics,2016,7(6):1005-1022.
[9] WU F X.Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties[J].IEEE Transactions on Biomedical Circuits & Systems,2011,5(4):391-398.
[10] LI Y J,ZHANG X,TAN C.Global exponential stability analysis of discrete-time genetic regulatory networks with time delays[J].Asian Journal of Control,2013,15(5):1448-1457.
[11] LI Z,CHEN D Y,ZHAO Y F.Robust stability analysis of delayed genetic regulatory networks with linear fractional parametric uncertainties[C]// Control and Decision Conference,August 8,2016,Las Vegas.USA∶IEEE,2016:1687-1692.
[12] LIU J L,YUE D.Asymptotical and robust stabilities of T-S fuzzy genetical regulatories network with time-varying-delays[J].International Journal of Robust Nonlinear Control,2012,22(8):827-840.
[13] 吴海霞,冯伟,冉维.时滞基因调控网络的全局渐近稳定性分析[J].计算机应用研究,2014,31(1):59-62.WU H X,FENG W,RAN W.Further analysis on global asymptotical stability of genetic regulatory networks with time delays[J].Application Research of Computers,2014,31(1):59-62.
[14] ZHOU Q,SHAO X Y,HAMID R K,et al.Stability of genetic regulatory networks with time-varying delay[J].Neurocomputing,2015,149(3):490-495.
[15] 张兴华,刘忠艳,叶明凤,等.不确定基因调控网络的保成本控制[J].黑龙江大学自然科学学报,2016,33(3):344-350.ZHANG X H,LIU Z Y,YE M F,et al.Guaranteed cost control for uncertain genetic regulatory networks[J].Journal of Natural Science of Heilongjiang University,2016,33(3):344-350.
[16] ZHANG Q,WEI X.Analysis on exponential stability of genetic regulatory networks with variable delays[J].Journal of Computational and Theoretical Nanoscience,2013,10(11):2604-2608.
[17] YUE D,TIAN E,ZHANG Y,et al.Delay-distribution-dependent robust stability of uncertain systems with time-varying delay[J].International Journal of Robust & Nonlinear Control,2010,19(4):377-393.
[18] XU S,CHEN T,LAM J.Robust H∞ H filtering for uncertain Markovian jump systems with mode-dependent time delays[J].IEEE Transactions on Automatic Control,2003,48(5):900-907.
[19] GU K,KHARITONOV V L,CHEN J.Stability of time-delay systems[M].Boston:Birkh?user,MA,2003.
[2] 王沛,吕金虎.基因调控网络的控制:机遇与挑战[J].自动化学报,2013,39(12):1969-1979.WANG P,LYU J H.Control of genetic regulatory networks:Opportunities and challenges[J].Acta Automatica Sinica,2013,39(12):1969-1979.
[3] 何勇,曾进,吴敏,等.具有区间时滞的离散时间基因调控网络稳定性研究[J].控制理论与应用,2012,29(11):1465-1470.HE Y,ZENG J,WU M,et al.Stability for discrete-time genetic regulatory networks with time-varying interval delays[J].Control Theory & Applications,2012,29(11):1465-1470.
[4] JIANG N,LIU X,YU W,et al.Finite-time stochastic synchronization of genetic regulatory networks[J].Neurocomputing,2015,167:314-321.
[5] WANG W,NGUANG S K,ZHONG S,et al.Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties[J].Communications in Nonlinear Science & Numerical Simulation,2014,19(5):1569-1581.
[6] LI C,CHEN L,AIHARA K.Synchronization of coupled nonidentical genetic oscillators[J].Physical Biology,2006,3(1):37-44.
[7] LOU X,YE Q,CUI B.Exponential stability of genetic regulatory networks with random delays[J].Neurocomputing,2010,73(4):759-769.
[8] ZHANG X,LI R,HAN C,et al.Robust stability analysis of uncertain genetic regulatory networks with mixed time delays[J].International Journal of Machine Learning & Cybernetics,2016,7(6):1005-1022.
[9] WU F X.Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties[J].IEEE Transactions on Biomedical Circuits & Systems,2011,5(4):391-398.
[10] LI Y J,ZHANG X,TAN C.Global exponential stability analysis of discrete-time genetic regulatory networks with time delays[J].Asian Journal of Control,2013,15(5):1448-1457.
[11] LI Z,CHEN D Y,ZHAO Y F.Robust stability analysis of delayed genetic regulatory networks with linear fractional parametric uncertainties[C]// Control and Decision Conference,August 8,2016,Las Vegas.USA∶IEEE,2016:1687-1692.
[12] LIU J L,YUE D.Asymptotical and robust stabilities of T-S fuzzy genetical regulatories network with time-varying-delays[J].International Journal of Robust Nonlinear Control,2012,22(8):827-840.
[13] 吴海霞,冯伟,冉维.时滞基因调控网络的全局渐近稳定性分析[J].计算机应用研究,2014,31(1):59-62.WU H X,FENG W,RAN W.Further analysis on global asymptotical stability of genetic regulatory networks with time delays[J].Application Research of Computers,2014,31(1):59-62.
[14] ZHOU Q,SHAO X Y,HAMID R K,et al.Stability of genetic regulatory networks with time-varying delay[J].Neurocomputing,2015,149(3):490-495.
[15] 张兴华,刘忠艳,叶明凤,等.不确定基因调控网络的保成本控制[J].黑龙江大学自然科学学报,2016,33(3):344-350.ZHANG X H,LIU Z Y,YE M F,et al.Guaranteed cost control for uncertain genetic regulatory networks[J].Journal of Natural Science of Heilongjiang University,2016,33(3):344-350.
[16] ZHANG Q,WEI X.Analysis on exponential stability of genetic regulatory networks with variable delays[J].Journal of Computational and Theoretical Nanoscience,2013,10(11):2604-2608.
[17] YUE D,TIAN E,ZHANG Y,et al.Delay-distribution-dependent robust stability of uncertain systems with time-varying delay[J].International Journal of Robust & Nonlinear Control,2010,19(4):377-393.
[18] XU S,CHEN T,LAM J.Robust H∞ H filtering for uncertain Markovian jump systems with mode-dependent time delays[J].IEEE Transactions on Automatic Control,2003,48(5):900-907.
[19] GU K,KHARITONOV V L,CHEN J.Stability of time-delay systems[M].Boston:Birkh?user,MA,2003.