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stability Criteria of Nonlinear Impulsive Differential Equations with Infinite Delays

Acta Mathematicae Applicatae Sinica 2015年第4期31卷 921-934页

作者： Yang LIU Bo WU Xiu-shan CAI Department of Mathematics Southeast University College of Mathematics Physics and Information EngineeringZhejiang Normal UniversityJinhua 321004China Graduate School Zhejiang Normal University

In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.

关键词： uniformly asymptotical stability impulsive differential equation infinite delay

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THE THEOREM OF THE stability OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 717-725页

作者：张书顺商大中 Haerbin Shipbuilding Engineering Institute Haerbin

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

关键词： nonautonomous system frequently-acting perturbation uniformly asymptotical stability state transition matrix

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stability in terms of two measures for impulsive stochastic functional differential systems with infinite delays

Stability in terms of two measures for impulsive stochastic ...

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第三十一届中国控制会议

作者： Fengqi Yao~1 Feiqi Deng~2 Hao Shen~1 1.School of Electrical Engineering & Information Anhui University of Technology Ma’anshan 243032 P.R.China 2.Institute of System Engineering South China University of Technology Guangzhou 510640 P.R.China

＜正＞This paper investigates the stability properties of impulsive stochastic functional differential systems with infinite *** employing piecewise continuous Lyapunov functions and the Razumikhin techniques,several criteria on uniform stability and uniformly asymptotical stability in terms of two measures for the mentioned systems are *** example is also worked out to illustrate our results.

关键词： Stochastic functional differential systems Impulsive differential systems Infinite delays uniformly asymptotical stability Razumikhin technique

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