New delay-decomposing method for stability analysis of genetic regulatory networks with time-varying delays
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- 英文论文题名：New delay-decomposing method for stability analysis of genetic regulatory networks with time-varying delays
- 论文作者：Jin Zhang ; Jinhai Zhang ; Liangdong Guo
- 英文论文作者：Jin Zhang ; Jinhai Zhang ; Liangdong Guo ; University of Science and Technology Liaoning
- 年：2017
- 作者机构：University of Science and Technology Liaoning;
- 英文论文关键词：Genetic Regulatory Networks ; Stability ; Time-varying delay ; Delay-decomposing method
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：142k
- 原文格式：D
- 会议级别：全国
摘要
The problem of the stability analysis of genetic regulatory networks(GRNs) with time varying delays are proposed in this paper based on a new delay-decomposing method.Some appropriate Lyapunov-krasovskiis functionals are defined on each of the obtained subintervals,some integral inequalities and the convex combination technique are utilized to deal with the bound of the derivative of the Lyapunov-krasovskiis functional.Then the criteria are derived in terms of linear matrix inequalities(LMIs).Finally,a numerical example is used to illustrate the usefulness and less conservative than relative references.
The problem of the stability analysis of genetic regulatory networks(GRNs) with time varying delays are proposed in this paper based on a new delay-decomposing method.Some appropriate Lyapunov-krasovskiis functionals are defined on each of the obtained subintervals,some integral inequalities and the convex combination technique are utilized to deal with the bound of the derivative of the Lyapunov-krasovskiis functional.Then the criteria are derived in terms of linear matrix inequalities(LMIs).Finally,a numerical example is used to illustrate the usefulness and less conservative than relative references.
The problem of the stability analysis of genetic regulatory networks(GRNs) with time varying delays are proposed in this paper based on a new delay-decomposing method.Some appropriate Lyapunov-krasovskiis functionals are defined on each of the obtained subintervals,some integral inequalities and the convex combination technique are utilized to deal with the bound of the derivative of the Lyapunov-krasovskiis functional.Then the criteria are derived in terms of linear matrix inequalities(LMIs).Finally,a numerical example is used to illustrate the usefulness and less conservative than relative references.
引文
[1]C.Li,L.Chen,K.Aihara,Stability of Genetic Networks With SUM Regulatory Logic:Lur'e System and LMI Approach,IEEE Trans.On Circuits&Systems,53(11):2451-2458,2006.
[2]X.Zhang,L.Wu,S.Cui,An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays,IEEE/ACM Trans,on Computational Biology&Bioinformatics,12(2):398-409,2015.
[3]W.Wang,S.Zhong,F.Liu,New delay-dependent stability criteria for uncertain genetic regulatory networks with time-varying delays,World Academy of Science Engineering&Technology,77(1):114-119,2012.
[4]W.Wang,S.Zhong,S.Nguang,Novel delay-dependent stability criterion for uncertain genetic regulatory networks with interval time-varying delays,Neurocomputing,121(18):170-178,2013.
[5]Z.Li,Y.Dong,R.Yu,New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays,Neurocomputing,207:763-771,2016.
[6]H.Wu,X.Liao,S.Guo,Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays,Neurocomputing,72(13-15):3263-3276,2009.
[7]W.Wang,S.Zhong,Delay-dependent stability criteria for genetic regulatory networks with time-varying delays and nonlinear disturbance,Communications in Nonlinear Science&Numerical Simulation,17(9):3597-3611,2012.
[8]Y.He,J.Zeng,M.Wu,Robust stabilization and H_∞controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,Mathematical Biosciences,236(1):53-63,2012.
[9]F.Ren,J.Cao,Asymptotic and robust stability of genetic regulatory networks with time-varying delays,The Chinese Control and Decision Conference,2008:527-531.(in Chinese)
[10]W.Zhang,J.Fang,Y.Tang,Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays,Applied Mathematics&Computation,217(17):7210-7225,2011.
[11]P.Balasubramaniam,R.Sathy,Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach,Communications in Nonlinear Science&Numerical Simulation,16(2):928-939,2011.
[12]L.Chen,K.Aihara,Stability of genetic regulatory networks with time delay,IEEE Trans,on Circuits&Systems I Fundamental Theory&Applications,49(5):602-608,2002.
[13]K.Gu,An integral inequality in the stability problem of time-delay systems,Proceedings of the Decision and Control,2000:2805-2810.
[14]L.Guo,H.Gu,J.Xing,Asymptotic and exponential stability of uncertain system with interval delay,Applied Mathematics&Computation,218(19):9997-10006,2012.
[15]L.Liu,Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay,Isa Transactions,53(6):1731-1738,2014.
[16]P.Park,J.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.
[2]X.Zhang,L.Wu,S.Cui,An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays,IEEE/ACM Trans,on Computational Biology&Bioinformatics,12(2):398-409,2015.
[3]W.Wang,S.Zhong,F.Liu,New delay-dependent stability criteria for uncertain genetic regulatory networks with time-varying delays,World Academy of Science Engineering&Technology,77(1):114-119,2012.
[4]W.Wang,S.Zhong,S.Nguang,Novel delay-dependent stability criterion for uncertain genetic regulatory networks with interval time-varying delays,Neurocomputing,121(18):170-178,2013.
[5]Z.Li,Y.Dong,R.Yu,New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays,Neurocomputing,207:763-771,2016.
[6]H.Wu,X.Liao,S.Guo,Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays,Neurocomputing,72(13-15):3263-3276,2009.
[7]W.Wang,S.Zhong,Delay-dependent stability criteria for genetic regulatory networks with time-varying delays and nonlinear disturbance,Communications in Nonlinear Science&Numerical Simulation,17(9):3597-3611,2012.
[8]Y.He,J.Zeng,M.Wu,Robust stabilization and H_∞controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,Mathematical Biosciences,236(1):53-63,2012.
[9]F.Ren,J.Cao,Asymptotic and robust stability of genetic regulatory networks with time-varying delays,The Chinese Control and Decision Conference,2008:527-531.(in Chinese)
[10]W.Zhang,J.Fang,Y.Tang,Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays,Applied Mathematics&Computation,217(17):7210-7225,2011.
[11]P.Balasubramaniam,R.Sathy,Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach,Communications in Nonlinear Science&Numerical Simulation,16(2):928-939,2011.
[12]L.Chen,K.Aihara,Stability of genetic regulatory networks with time delay,IEEE Trans,on Circuits&Systems I Fundamental Theory&Applications,49(5):602-608,2002.
[13]K.Gu,An integral inequality in the stability problem of time-delay systems,Proceedings of the Decision and Control,2000:2805-2810.
[14]L.Guo,H.Gu,J.Xing,Asymptotic and exponential stability of uncertain system with interval delay,Applied Mathematics&Computation,218(19):9997-10006,2012.
[15]L.Liu,Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay,Isa Transactions,53(6):1731-1738,2014.
[16]P.Park,J.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.