Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are stud...Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.展开更多
In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established...In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.展开更多
A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered...A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.展开更多
By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neu...By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.展开更多
The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive diff...The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.展开更多
In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than th...In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.展开更多
So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It...So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.展开更多
The stabilization problem of a nonuniform Timoshenko beam system with controllers at the beam's right tip with rotor inertia is studied.First,with a special kind of linear boundary force feedback and moment contro...The stabilization problem of a nonuniform Timoshenko beam system with controllers at the beam's right tip with rotor inertia is studied.First,with a special kind of linear boundary force feedback and moment control existing simultaneously,the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t→∞.Then in other cases,some conditions for the corresponding closed loop system to be asymptotically stable are also derived.展开更多
基金partially supported by Fund Scientific Research MU15FMIIT008,Plovdiv University
文摘Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.
基金Supported by the National Natural Science Foundation of China(11301004,61403002,61273126)the Anhui Provincial Nature Science Foundation(1308085QA15,1308085MA01,1508085QA01)+3 种基金the Excellent Youthful Talent Foundation of Colleges and Universities of Anhui Province of China(2013SQRL024ZD)the Postdoctoral Sus-tentation Fund of Jiangsu Province of China(1402021C)Provincial Natural Science Research Project of Anhui Colleges(KJ2014A010)Research Fund for Doctor Station of Ministry of Education of China(20113401110001)
文摘A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.
基金supported by Natural Science Foundation of Hebei Province under Grant No.E2007000381
文摘By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.
基金Supported by the National Natural Science Foundation of China (Grant No. 10772046)
文摘The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.
基金Supported by the National Natural Science Foundation of China (Grant Nos.6073602930570507)the National Basic Research Program of China (Grant No.2010CB732501)
文摘In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.
基金Supported by the National Natural Science Foundation of China(Grant No.60574042)
文摘So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
基金This research is supported by the National Natural Science Foundation of China (00174008).
文摘The stabilization problem of a nonuniform Timoshenko beam system with controllers at the beam's right tip with rotor inertia is studied.First,with a special kind of linear boundary force feedback and moment control existing simultaneously,the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t→∞.Then in other cases,some conditions for the corresponding closed loop system to be asymptotically stable are also derived.
