This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Li...This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Lipschitz condition for activation function is also relaxed.Second,different from the traditional Lyapunov function,two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization.Significantly,the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states.In addition,the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance.Especially,the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization.Furthermore,the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control.Finally,examples show the effectiveness of the proposed control methods.展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neur...Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.展开更多
This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory i...This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory in set-valued analysis,we have established the existence of the bounded positive periodic solutions for the addressed models.After that,based on the nonsmooth analysis theory w让 h Lyapunov-like approach,we employ a novel argument and derive some new criteria on the uniqueness,global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models.Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended.In addition,typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results.展开更多
By using the continuation theorem of Mawhin＇s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stab...By using the continuation theorem of Mawhin＇s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.展开更多
基金National Natural Science Foundation of China under Grants 62203338,61936004,61821003,62173259 and 62176192Postdoctoral Science Foundation of China under Grant 2022M722485.
文摘This paper investigates the exponential and prescribed finite-time stabilization with time-varying controller.First,the constraints of boundedness and differentiability on time delays are simultaneously relaxed,the Lipschitz condition for activation function is also relaxed.Second,different from the traditional Lyapunov function,two different time-varying Lyapunov functions are respectively constructed to achieve the exponential and prescribed finite-time stabilization.Significantly,the exponential convergence rate and the settling time are constants that can be given in advance and are not affected by system parameters and initial states.In addition,the time-varying controllers have good tolerance for disturbance caused by discontinuous functions and the disturbance is perfectly resolved and does not affect the control performance.Especially,the form of controllers is relatively simple and there is not necessary to design the fractional-order controllers for prescribed finite-time stabilization.Furthermore,the exponential and prescribed finite-time stabilization for FNNs without delay are respectively established via continuous time-varying state feedback control.Finally,examples show the effectiveness of the proposed control methods.
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
文摘Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.
文摘This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms.Under the framework of Filippov solution,by means of the differential inclusions and the topological degree theory in set-valued analysis,we have established the existence of the bounded positive periodic solutions for the addressed models.After that,based on the nonsmooth analysis theory w让 h Lyapunov-like approach,we employ a novel argument and derive some new criteria on the uniqueness,global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models.Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended.In addition,typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results.
基金Supported by the National Natural Science Foundation of China (No. 10971173)the Scientific Research Foundation of Hunan Provincial Educational Department (No. 05A057)+1 种基金supported by the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Provincethe Construct Program of the Key Discipline in Hunan Province
文摘By using the continuation theorem of Mawhin＇s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.
