In this paper, we investigate the description of T-B singularity and the bifurcation behavior near T-B point for delay differential systems with two parameters.
In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solutio...In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.展开更多
In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigat...In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.展开更多
The problem of delay-dependent robust stability for uncertain linear singular neutral systems with time-varying and distributed delays is investigated. The uncertainties under consideration are norm bounded,and possib...The problem of delay-dependent robust stability for uncertain linear singular neutral systems with time-varying and distributed delays is investigated. The uncertainties under consideration are norm bounded,and possibly time varying. Some new stability criteria,which are simpler and less conservative than existing results,are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coeffcient matrix and formulated in...展开更多
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of mat...In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.展开更多
Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying t...Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.展开更多
主要研究三重零奇异的判定和在R^n上零特征根对应的广义特征空间,利用中心流形简化和规范型计算得到参数时滞微分方程的简化形式,对应于文[A note on the triple zero linear degeneracy:Normal forms,dynamical and bifurcation behavi...主要研究三重零奇异的判定和在R^n上零特征根对应的广义特征空间,利用中心流形简化和规范型计算得到参数时滞微分方程的简化形式,对应于文[A note on the triple zero linear degeneracy:Normal forms,dynamical and bifurcation behaviour of an unfolding.Int J Bifur and Chaos,2002,12:2799-2820]中的结果具体分析具有三重零奇异的参数时滞微分方程的分支行为,并给出一例子来阐述得到的结果.展开更多
The stability of differential-algebraic equations (DAEs) was analyzed using singularity induced bifurcation (SIB) with one parameter. This kind of bifurcation arises in parameter-dependent DAEs having the form x·...The stability of differential-algebraic equations (DAEs) was analyzed using singularity induced bifurcation (SIB) with one parameter. This kind of bifurcation arises in parameter-dependent DAEs having the form x·=f, 0=g. Extended DAE system reduction is introduced as a convenient method to compute the SIB points. Non-degeneracy conditions on the function g are needed. Aften verifying these conditions, the extended DAE system can be solved as an ODE by applying the implicit function theorem near the equilibrium point of the extended DAE system. These equilibrium points in turn include the SIB points of the original DAEs. The study of SIB points enables analysis of power system stability problems.展开更多
文摘In this paper, we investigate the description of T-B singularity and the bifurcation behavior near T-B point for delay differential systems with two parameters.
基金Supported by the National Natural Science Foundation of China (No.10771001)the Key Program of Ministry of Education of China (No.205068)+1 种基金the Foundation of Education Department of Anhui Province (No.KJ2008B152)the Foundation of Innovation Team of Anhui University.
文摘In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.
基金Supported by the National Natural Science Foundation of China (Grant No.10771001)the Special Research Fund for the Doctoral Program of Higher Education of China (Grant No.20093401110001)+3 种基金the Natural Science Key Foundation of Education Department of Anhui Province (Grant No.KJ2010ZD02)the Natural Science Foundation of Education Department of Anhui Province (Grant Nos.KJ2008B152 KJ2009B098)the Foundation of Innovation Team of Anhui University
文摘In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.
基金Supported by the National Natural Science Foundation of China (10771001)the Key Program of Ministry of Education of China (205068)the Foundation of Innovation Team of Anhui Univ
文摘The problem of delay-dependent robust stability for uncertain linear singular neutral systems with time-varying and distributed delays is investigated. The uncertainties under consideration are norm bounded,and possibly time varying. Some new stability criteria,which are simpler and less conservative than existing results,are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coeffcient matrix and formulated in...
基金Supported by the National Natural Science Foundation of China (10771001)the Key Program of Ministry of Education of China (205068)
文摘In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
基金supported by the National Natural Science Foundation of China(No.10771001)the Key Program of Ministry of Education of China (No.205068)the Programof Innovation Team of University of Anhui
文摘Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.
文摘主要研究三重零奇异的判定和在R^n上零特征根对应的广义特征空间,利用中心流形简化和规范型计算得到参数时滞微分方程的简化形式,对应于文[A note on the triple zero linear degeneracy:Normal forms,dynamical and bifurcation behaviour of an unfolding.Int J Bifur and Chaos,2002,12:2799-2820]中的结果具体分析具有三重零奇异的参数时滞微分方程的分支行为,并给出一例子来阐述得到的结果.
基金Supported by the National Special Fund for Key BasicResearch of China(No.19980 2 0 30 9)
文摘The stability of differential-algebraic equations (DAEs) was analyzed using singularity induced bifurcation (SIB) with one parameter. This kind of bifurcation arises in parameter-dependent DAEs having the form x·=f, 0=g. Extended DAE system reduction is introduced as a convenient method to compute the SIB points. Non-degeneracy conditions on the function g are needed. Aften verifying these conditions, the extended DAE system can be solved as an ODE by applying the implicit function theorem near the equilibrium point of the extended DAE system. These equilibrium points in turn include the SIB points of the original DAEs. The study of SIB points enables analysis of power system stability problems.
