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
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
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
In this article we consider a transmission problem with memory in a bounded domain and varying delay term in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we ...In this article we consider a transmission problem with memory in a bounded domain and varying delay term in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we show the exponential sta- bility of the solution by introducing a suitable Lyapunov functional.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.
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.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.
文摘In this article we consider a transmission problem with memory in a bounded domain and varying delay term in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we show the exponential sta- bility of the solution by introducing a suitable Lyapunov functional.
