It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.
Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the m...Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.展开更多
Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergen...Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.展开更多
We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite soluti...We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function.Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.展开更多
In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to pr...In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.展开更多
In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asympt...Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.展开更多
In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species ca...In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore~ some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.展开更多
In this paper, we consider a predator-prey model. A sufficient conditionis presented for the stability of the equilibrium, which is different from the one for themodel with Hassell-Varley type functional response. Fur...In this paper, we consider a predator-prey model. A sufficient conditionis presented for the stability of the equilibrium, which is different from the one for themodel with Hassell-Varley type functional response. Furthermore, by constructing aLyapunov function, we prove that the positive equilibrium is asymptotically stable.展开更多
This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.
In this paper,we propose a semi-continuous dynamical system to study the cooperative system with feedback control.Based on geometrical analysis and the analogue of Poincaré criterion,the existence and stability o...In this paper,we propose a semi-continuous dynamical system to study the cooperative system with feedback control.Based on geometrical analysis and the analogue of Poincaré criterion,the existence and stability of the positive order one periodic solutions are given.Numerical results are carried out to illustrate the feasibility of our main results.展开更多
In this paper, the problems of the stability analysis and BIBO stabilization for the switched systems are considered. Applying a stabilizing local state feedback to each subsystem, the sufficient conditions of the asy...In this paper, the problems of the stability analysis and BIBO stabilization for the switched systems are considered. Applying a stabilizing local state feedback to each subsystem, the sufficient conditions of the asymptotically stable and BIBO stabilization for the switched systems are obtained by means of the method of Lyapunov function and the method of inequality analysis.展开更多
In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than th...In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.展开更多
In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a...In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale＇s invariance principle in difference equation is applied.展开更多
By using Lyapunov function and differential inequality, sufficient conditions for the existence of global asymptotical stable almost periodic solution of the three-species almost periodic modei with the type II functi...By using Lyapunov function and differential inequality, sufficient conditions for the existence of global asymptotical stable almost periodic solution of the three-species almost periodic modei with the type II functional response are obtained.展开更多
In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot d...In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].展开更多
We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' ...We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' + g(x) = e(t) has uniformly asymptotically stable solutions if g(0) = 0, and Hence it has a unique almost odic solution when e(t) is almost periodic and it has a unique periodic solution when e(t) is periodic. In [1] Fink obtained above the second conclusion if sup In [2] we obtained same result if g(x) = cx.展开更多
A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally as...A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.展开更多
This paper studies the extension of LaSalle＇s invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper...This paper studies the extension of LaSalle＇s invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle＇s invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.展开更多
基金This work is partially supported by D.G.Y.C.T.PB 96-1338-CO 2-01 and the Junta de Andalucía.
文摘It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.
基金This project was supported by the National Natural Science Foundation of China (60274014, 60574088).
文摘Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.
基金Project supported by the National Science Fund for distinguished Young Scholars of China (Grant No 60525303)the Specialized Research Fund for the Doctoral Program of High Education of China (Grant No 20050216001)
文摘Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.
文摘We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function.Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.
基金the National Natural Science Foundation of China (No. 10671069, 60674046)
文摘In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.
文摘In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.
文摘Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
基金Supported-by the Start-up Fund of Jimei University(ZB2004009)
文摘In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore~ some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.
文摘In this paper, we consider a predator-prey model. A sufficient conditionis presented for the stability of the equilibrium, which is different from the one for themodel with Hassell-Varley type functional response. Furthermore, by constructing aLyapunov function, we prove that the positive equilibrium is asymptotically stable.
文摘This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.
基金Supported by the National Natural Science Foundation of China(11671346,11501489,11371306,11301453)Supported by the Department of Education of Henan Province(14B110034)+1 种基金Supported by the Nanhu Scholars Program of XYNU,Foundation and Frontier Project of Henan(152300410019)Supported by the Youth Teacher Foundation of XYNU(2016GGJJ-14)
文摘In this paper,we propose a semi-continuous dynamical system to study the cooperative system with feedback control.Based on geometrical analysis and the analogue of Poincaré criterion,the existence and stability of the positive order one periodic solutions are given.Numerical results are carried out to illustrate the feasibility of our main results.
文摘In this paper, the problems of the stability analysis and BIBO stabilization for the switched systems are considered. Applying a stabilizing local state feedback to each subsystem, the sufficient conditions of the asymptotically stable and BIBO stabilization for the switched systems are obtained by means of the method of Lyapunov function and the method of inequality analysis.
基金Supported by the National Natural Science Foundation of China (Grant Nos.6073602930570507)the National Basic Research Program of China (Grant No.2010CB732501)
文摘In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.
文摘In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale＇s invariance principle in difference equation is applied.
基金Supported by the Foundation of the Education Department of Fujian Province(JB01023).
文摘By using Lyapunov function and differential inequality, sufficient conditions for the existence of global asymptotical stable almost periodic solution of the three-species almost periodic modei with the type II functional response are obtained.
文摘In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].
文摘We consider Lienard system and obtain following conclusions: The zero solution of system x' + f(x)x' + g(x) = 0 is uniformly asymptotically stable if g(0) = 0, and (x) > 0. And system X' + f(x)x' + g(x) = e(t) has uniformly asymptotically stable solutions if g(0) = 0, and Hence it has a unique almost odic solution when e(t) is almost periodic and it has a unique periodic solution when e(t) is periodic. In [1] Fink obtained above the second conclusion if sup In [2] we obtained same result if g(x) = cx.
基金Supported by National Natural Science Foundation of China (Grant No. 10971021)the Ministry of Education of China (Grant No. 109051)+1 种基金the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918)the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)
文摘A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 60221301, 60674022 and 60736022)
文摘This paper studies the extension of LaSalle＇s invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle＇s invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.
