This paper is devoted to the investigation of Lyapunov's second method for the stability of measure differential large scale systems containing impulses. The vector comparison principle of the stability of measur...This paper is devoted to the investigation of Lyapunov's second method for the stability of measure differential large scale systems containing impulses. The vector comparison principle of the stability of measure differential large scale systems is first established. An application of the vector comparison theorem is given to demonstrate the effectiveness of our result.展开更多
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
文摘This paper is devoted to the investigation of Lyapunov's second method for the stability of measure differential large scale systems containing impulses. The vector comparison principle of the stability of measure differential large scale systems is first established. An application of the vector comparison theorem is given to demonstrate the effectiveness of our result.
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.
