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1.
Stability of impulsive functional differential equations 总被引:1,自引:0,他引:1
In this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied. By using Lyapunov functions and Razumikhin techniques, some criteria of stability, asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided. Some examples are also presented to illustrate the efficiency of the results obtained. 相似文献
2.
In this paper, we investigate the existence of solutions of impulsive delay differential equation
3.
Qing Wang 《Journal of Mathematical Analysis and Applications》2005,309(2):462-473
In this paper, we study exponential stability for impulsive delay differential equation of the form
4.
Yu Zhang 《Journal of Mathematical Analysis and Applications》2005,301(1):237-248
Strict stability is the kind of stability that can give us some information about the rate of decay of the solutions. There are some results about strict stability of differential equations. In the present paper, we shall extend the strict stability to impulsive functional differential equations. By using Lyapunov functions and Razumikhin technique, we shall get some criteria for the strict stability of impulsive functional differential equations, and we can see that impulses do contribute to the system's strict stability behavior. 相似文献
5.
Shenglan Xie 《Applied mathematics and computation》2011,218(2):592-597
In this paper, we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous Lyapunov functions with Razumickhin techniques. Some sufficient conditions for stability of sets are established, and some known stability theorems also are generalized. 相似文献
6.
LuoZhiguo ShenJianhua 《高校应用数学学报(英文版)》2005,20(2):142-150
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. 相似文献
7.
Jianhua Shen 《Journal of Mathematical Analysis and Applications》2006,314(2):546-557
This paper studies the global existence of solutions of the impulsive differential equation
8.
This article establishes mean square stability and stabilization for stochastic delay systems with impulses. Using Razumikhin methodology, two approaches, classical Lyapunov-based method and comparison principle, are proposed to develop sufficient conditions that guarantee the stability and stabilization properties. It is shown that if the continuous system is stable and the impulses are destabilizing, the impulses should not be applied frequently. On the other hand, if the continuous system is unstable, but the impulses are stabilizing, the impulses should occur frequently to compensate the continuous state growth. Numerical examples are also presented to clarify the proposed theoretical results. 相似文献
9.
In this paper, we study the stability of nonlinear impulsive stochastic differential equations in terms of two measures. The concept of perturbing Lyapunov functions is introduced to discuss stability properties of solutions of nonlinear impulsive stochastic differential equations in terms of two measures. By using perturbing Lyapunov functions and comparison method, some sufficient conditions for the above stability are given. 相似文献
10.
Stability caused by impulses for delay differential equations 总被引:3,自引:0,他引:3
Yu Jianshe 《数学学报(英文版)》1997,13(2):193-198
In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential
equation caused by impulses.
This work is partially supported by NNSF of China and EYTF of National Educational Committee 相似文献
11.
In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results. 相似文献
12.
Xiaodi Li 《Applied Mathematics Letters》2012,25(2):133-137
A criterion for the uniform stability of impulsive functional differential equations with infinite delays is presented by using Lyapunov functions and the Razumikhin technique. The criterion is more general than several recent works. An example showing the effectiveness and advantage of the present criterion is given. 相似文献
13.
为研究积分-微分系统的稳定性,运用Lyapunov函数直接方法并借助Razumikhin技巧的思想,通过减弱Lyapunov函数沿系统解的导数须常负或定负的限制条件,给出了判断脉冲积分-微分系统零解稳定性的新的直接判定定理. 相似文献
14.
In this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
本文讨论了一类Rosenbrock方法求解比例延迟微分方程,y′(t)=λy(t) μy(qt),λ,μ∈C,0 相似文献
16.
The present paper deals with the investigation of the stability of the zero solution of impulsive functional differential equations. By means of piecewise continuous functions coupled with the Razumikhin technique sufficient conditions for stability, uniform stability and asymptotic stability of the zero solution of such equations are found. 相似文献
17.
In this note, we study the exponential stability of impulsive functional differential systems with infinite delays by using the Razumikhin technique and Lyapunov functions. Several Razumikhin-type theorems on exponential stability are obtained, which shows that certain impulsive perturbations may make unstable systems exponentially stable. Some examples are discussed to illustrate our results. 相似文献
18.
G.Sh. Guseinov 《Journal of Mathematical Analysis and Applications》2007,335(2):1195-1206
In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. 相似文献
19.
This paper considers general impulsive delay differential equations. By utilizing a non-classical approach, the theory of existence and uniqueness of solutions are developed. Criteria on boundedness of solutions are also established through the use of Lyapunov functionals. 相似文献
20.
This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system. 相似文献