In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The co...In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.展开更多
Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some r...Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.展开更多
This paper investigates the stability of impulsive linear hybrid systems with time delay.And a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov functio...This paper investigates the stability of impulsive linear hybrid systems with time delay.And a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov functionals.Two examples are also presented to illustrate the effectiveness ofthe obtained results or to compare with the existing results.展开更多
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005)the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244)
文摘In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.
基金A project supported by Scientific Research Fund of Hunan Provincial Education Department.
文摘Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10926114, 60874027, 60904027the "Chen Guang" project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation
文摘This paper investigates the stability of impulsive linear hybrid systems with time delay.And a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov functionals.Two examples are also presented to illustrate the effectiveness ofthe obtained results or to compare with the existing results.
