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 stability of a class of impulsive functional differential equations with infinite delays is investigated.A uniform stability theorem and a uniform asymptotic stability theorem are established.
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
Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems...Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems to some nonlinear differential systems with infinite delay are discussed.展开更多
By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improv...By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.展开更多
In this paper, we study the boundedness of a class of impulsive functional differential equations with infinite delays. We establish a uniform boundedness theorem and a uniformly ultimate boundedness theorem, which sh...In this paper, we study the boundedness of a class of impulsive functional differential equations with infinite delays. We establish a uniform boundedness theorem and a uniformly ultimate boundedness theorem, which show that a certain impulsive perturbation can make an unbounded system into uniformly bounded, even uniformly ultimate bounded.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.
文摘In this paper,the stability of a class of impulsive functional differential equations with infinite delays is investigated.A uniform stability theorem and a uniform asymptotic stability theorem are established.
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.
基金Project supported by the National Science Foundation of China Under Grants 69871005
文摘Two families of Liapunov functions are employed to study the global stability and bound- edness of functional differential systems. New stability and boundedness theorems are obtained. Ap- plications of these theorems to some nonlinear differential systems with infinite delay are discussed.
基金Supported by the National Natural Science Foundation of China (Grant No.60973048)the Natural Science Foundation of Shandong Province (Grant No.Y2007G30)the Young Science Foundation of Qingdao University
文摘By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.
文摘In this paper, we study the boundedness of a class of impulsive functional differential equations with infinite delays. We establish a uniform boundedness theorem and a uniformly ultimate boundedness theorem, which show that a certain impulsive perturbation can make an unbounded system into uniformly bounded, even uniformly ultimate bounded.
