In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is ...In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is considered in the model,as fear can reduce the reproduction rate and disease transmission rate among prey.First,some basic mathematical results of the proposed model are discussed.Then,time delay is regarded as a bifurcation parameter,and the delay-induced bifurcation conditions for such an uncontrolled system are established.A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon.It is found that the control scheme can successfully suppress the bifurcation behavior of the system,and the pulse width can be arbitrarily selected on the premise of ensuring the control effect.Compared with the traditional time-delay feedback controller,the control scheme proposed in this paper has more advantages in practical application,which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment.The proposed control scheme,in particular,remains effective even after the system has been disrupted by a constant.Numerical simulation verifies the correctness of the theoretical results.展开更多
In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient condit...In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem.All the results are obtained in terms of linear matrix inequalities that are numerically tractable.The proposed results are quite general and improve those given in the literature since many factors,such as discrete and distributed delays,convex polytopic uncertainties,global stability and stabilizability,are considered.Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.展开更多
In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to for...In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.展开更多
In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the correspondin...In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.展开更多
基金supported by Liaoning Provincial Department of Education Scientific Research Fund Project(lnjc202018).
文摘In this paper,a new delayed fractional-order model including susceptible migratory birds,infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds.Fear of predators is considered in the model,as fear can reduce the reproduction rate and disease transmission rate among prey.First,some basic mathematical results of the proposed model are discussed.Then,time delay is regarded as a bifurcation parameter,and the delay-induced bifurcation conditions for such an uncontrolled system are established.A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon.It is found that the control scheme can successfully suppress the bifurcation behavior of the system,and the pulse width can be arbitrarily selected on the premise of ensuring the control effect.Compared with the traditional time-delay feedback controller,the control scheme proposed in this paper has more advantages in practical application,which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment.The proposed control scheme,in particular,remains effective even after the system has been disrupted by a constant.Numerical simulation verifies the correctness of the theoretical results.
基金supported by Ministry of Education and Training of Vietnam(B2020-TNA)。
文摘In this paper,the problems of robust stability and stabilization,for the first time,are studied for delayed fractional-order linear systems with convex polytopic uncertainties.The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem.All the results are obtained in terms of linear matrix inequalities that are numerically tractable.The proposed results are quite general and improve those given in the literature since many factors,such as discrete and distributed delays,convex polytopic uncertainties,global stability and stabilizability,are considered.Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.
基金co-supported by the National Natural Science Foundation of China (Nos. 61333011, 91216304 and 61121003)
文摘In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.
基金National Natural Science Foundation of China (10671069)Shanghai LeadingAcademic Discipline Project (B407).
文摘In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.
