In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying ...In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.展开更多
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and alm...The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.展开更多
This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and di...This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameterdependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.展开更多
In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of th...In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.展开更多
In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding ...In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.展开更多
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reac...In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.展开更多
In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of posit...In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.展开更多
基金the Scientific Innovation Team Project of Hubei Provincial Department of Education (T200809)the Science Foundationof Education Commission of Hubei Province (No. D20081306)the Doctoral Pre-research Foundation of Three Gorges University
文摘In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.
基金Project supported by the National Natural Science Foundation of China (No.60574025)the Natural Science Foundation of Hubei Province of China (Nos.2004ABA055, D200613002)the Natural Science Foundation of China Three Gorges University.
文摘The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.
基金This work was supported by the Science Foundation of Education Commission of Hubei Province(No.D200613002)the Doctoral Pre-ResearchFoundation of Three Gorges University.
文摘This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameterdependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.
基金the National Natural Science Foundation of China 10471022the Ministry of Education of China Science and Technology Major Projects Grant 104090the Foundation of Excellent Doctoral Disscrtation of Southeast University YBJJ0405
文摘In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.
基金supported by National Natural Science Foundation of China (Grant Nos. 10801090, 10871185, 10726016)supported by the Scientifio Research Projects of Hubei Provincial Department of Education (Grant No. Q200713001)+1 种基金Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No. T200809)supported by National Natural Science Foundation of China (Grant No. 10771032)
文摘In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.
基金the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032)the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)
文摘In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
基金This work Was partially supported by the National Natural Science Foundation of China(Grant No.10471022)
文摘In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.
