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
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel cha...Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.展开更多
This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such a...This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.展开更多
Sufficient conditions for the exponentially asymptotic stability of the trivial solutionof the following nonlinear neutral differential difference system:[x(t)-cx(t-r(t))]'= f(t, x(t), x(t-r(t)).are obtained.
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.
The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbanc...The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbance,the solution for the system is discontinuous.By using the Razumikhin technique and stochastic analysis approaches,as well as combining the idea of mathematical induction and classification discussion,some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained.The stability conclusion is full time-delay.The results show that impulse,the point distance of impulse and Markovain switching affect the stability for the system.Finally,two examples are provided to illustrate the effectiveness of the results proposed.展开更多
In this paper, we consider neutral functional differential equations with infinite delay. Sufficient and necessary criteria for the g-uniform asymptotic stability of solutions to the system in the phase space (Cg,|...In this paper, we consider neutral functional differential equations with infinite delay. Sufficient and necessary criteria for the g-uniform asymptotic stability of solutions to the system in the phase space (Cg,|·|g) are established.展开更多
In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay a...In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay and degenerate neutral differential systems with delay.Also,we give an example to illustrate the main results.展开更多
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical result...The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.展开更多
A series of eontractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundatio...A series of eontractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs), neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.展开更多
This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcom...This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.展开更多
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...
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
文摘Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.
基金Supported by NSF of Guangdong Province(O11471)and Higher Education Bureau(0120).
文摘Sufficient conditions for the exponentially asymptotic stability of the trivial solutionof the following nonlinear neutral differential difference system:[x(t)-cx(t-r(t))]'= f(t, x(t), x(t-r(t)).are obtained.
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
基金Sponsored by HUST Foundation(0125011017)the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
基金Sponsored by HUST Foundation(0125011017) the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
文摘In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.
基金This research was supported by the National Nature Science Foundation of China under Grant No.11571245Young Crop Project of Sichuan University under Grant No.2020SCUNL111.
文摘The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbance,the solution for the system is discontinuous.By using the Razumikhin technique and stochastic analysis approaches,as well as combining the idea of mathematical induction and classification discussion,some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained.The stability conclusion is full time-delay.The results show that impulse,the point distance of impulse and Markovain switching affect the stability for the system.Finally,two examples are provided to illustrate the effectiveness of the results proposed.
文摘In this paper, we consider neutral functional differential equations with infinite delay. Sufficient and necessary criteria for the g-uniform asymptotic stability of solutions to the system in the phase space (Cg,|·|g) are established.
基金Supported by the National Natural Science Foundation of China (10771001)the Key Program of Ministry of Education of China(205068)+1 种基金the Foundation of Education Department of Anhui Province (KJ2008B152)the Foundation of Innovation Group of Anhui University.
文摘In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay and degenerate neutral differential systems with delay.Also,we give an example to illustrate the main results.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.10271100 and 10571147)
文摘The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
基金Supported by the National Natural Science Foundation of China (No. 11001033)Natural Science Foundation of Hunan Province (No. 10JJ4003)+3 种基金the Open Fund Project of Key Research Institute of Philosophies and Social Sciences in Hunan Universitiesthe Major Foundation of Educational Committee of Hunan Province(No. 09A002 [2009])the Scientific Innovation Foundation for the Electric Power Youth of Chinese Society for Electrical Engineeringthe Science and Technology Planning Project of Hunan Province (No. 2010SK3026)
文摘A series of eontractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs), neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
文摘This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.
基金E-Institutes of Shanghai Municipal Education Commission (E03004) Shanghai Municipal Education Commission (04DB07)+1 种基金 Shanghai Science and Technology Committee (03QA14036) NSFC (10671130) and the Special Funds for Major Specialties of Shanghai Education Committee