Sufficient conditions for the exponentially asymptotic stability of the trivial solutionof the following nonlinear neutral differential difference system:[x(t)-cx(t-r(t))]'= f(t, x(t), x(t-r(t)).are obtained.
Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condit...Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.展开更多
This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line functi...This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function, some criteria of global exponential asymptotic stability for the impulsive time-delay system are established. An example is given to illustrate the applicability of the obtained results.展开更多
This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcom...This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.展开更多
This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and glob...This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks.展开更多
In this paper, by using phase space (Ch,｜·｜h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with in...In this paper, by using phase space (Ch,｜·｜h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with infinite delay. By combining properties of space Ch and some techniques of Liapunov functional, we show that the h-exponentially asymptotical stability of solutions for the equations implies the existence of the bounded solutions and it guarantees the existence of the almost periodic solutions for the equations.展开更多
基金Supported by NSF of Guangdong Province(O11471)and Higher Education Bureau(0120).
文摘Sufficient conditions for the exponentially asymptotic stability of the trivial solutionof the following nonlinear neutral differential difference system:[x(t)-cx(t-r(t))]'= f(t, x(t), x(t-r(t)).are obtained.
文摘Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.
文摘This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function, some criteria of global exponential asymptotic stability for the impulsive time-delay system are established. An example is given to illustrate the applicability of the obtained results.
文摘This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.
基金supported by National Natural Science Foundation of China under Grant 61573005 and 11361010the Foundation for Young Professors of Jimei Universitythe Foundation of Fujian Higher Education(JA11154,JA11144)
文摘This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks.
文摘In this paper, by using phase space (Ch,｜·｜h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with infinite delay. By combining properties of space Ch and some techniques of Liapunov functional, we show that the h-exponentially asymptotical stability of solutions for the equations implies the existence of the bounded solutions and it guarantees the existence of the almost periodic solutions for the equations.
