In this paper, we investigate the solution moment stability for a Harrison-type predator-prey model with parametric dichotomous noises. Using the Shapiro-Loginov formula, the equations for the first-order and second-o...In this paper, we investigate the solution moment stability for a Harrison-type predator-prey model with parametric dichotomous noises. Using the Shapiro-Loginov formula, the equations for the first-order and second-order moments are obtained and the corresponding stable conditions are given. It is found that the solution moment stability depends on the noise intensity and correlation time of noise. The first-order and second-order moments become unstable with the decrease of correlation time. That is, the dichotomous noise can improve the solution moment stability with respect to Gaussian white noise. Finally, some numerical results are presented to verify the theoretical analyses.展开更多
This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some suffi...This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.展开更多
The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observat...The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observations.The upper bound on the duration between two consecutive observations is obtained as well.Finally,a numerical example is given to verify the validity of the theoretical conclusions.展开更多
In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switch...In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.展开更多
This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations wi...This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.展开更多
Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros (SGCMGs) as actuators is investigated. First of all, the dy...Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros (SGCMGs) as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.展开更多
This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ...This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.展开更多
This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such a...This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.展开更多
We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and st...We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.展开更多
This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in outp...This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11272051)
文摘In this paper, we investigate the solution moment stability for a Harrison-type predator-prey model with parametric dichotomous noises. Using the Shapiro-Loginov formula, the equations for the first-order and second-order moments are obtained and the corresponding stable conditions are given. It is found that the solution moment stability depends on the noise intensity and correlation time of noise. The first-order and second-order moments become unstable with the decrease of correlation time. That is, the dichotomous noise can improve the solution moment stability with respect to Gaussian white noise. Finally, some numerical results are presented to verify the theoretical analyses.
文摘This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.
文摘The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observations.The upper bound on the duration between two consecutive observations is obtained as well.Finally,a numerical example is given to verify the validity of the theoretical conclusions.
文摘In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.
文摘Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros (SGCMGs) as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.
文摘This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.
文摘We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.
基金supported by National Basic Research Program of China(973 Program)(No.2012CB821205)National Natural Science Foundation of China(Nos.61021002 and 61203125)Fundamental Research Funds for the Central Universities(No.HIT.NSRIF.2013039)
文摘This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.