The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient...The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient conditions of the uniformly stability and the global exponentially stability are given for the above systems through defining a Lyapunov function of the weighting sum of the variable absolute by using the Lyapunov function method and the comparison principle. At the same time, the new conclusion of stability of these systems is more universal and contains the existing results. Finally, an example is given to illustrate the feasibility and validity of the obtained results.展开更多
Many impulsive phenomena from physics, control theory, and economics urge us toinvestigate measure large scale systems. In this paper, the variation of parameters formulaof the large scale systems containing measures ...Many impulsive phenomena from physics, control theory, and economics urge us toinvestigate measure large scale systems. In this paper, the variation of parameters formulaof the large scale systems containing measures is established. By means of inequality methods and comparison theory, the stability, uniform stability, asymptotic stability, uniformasymptotic stability, and exponential stability properties of linear measure large scale systems are studied.展开更多
This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula ...This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula of large scale singular systems containing measures and delays is obtained.Employing inequality methods and comparison theory,the stability properties of large scale systems are studied.展开更多
In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable...In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.展开更多
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
基金Project (60674020) supported by the National Natural Science Foundation of ChinaProject (Z2006G11) supported by Specialized Natural Science Fund of Shandong Province,China
文摘The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient conditions of the uniformly stability and the global exponentially stability are given for the above systems through defining a Lyapunov function of the weighting sum of the variable absolute by using the Lyapunov function method and the comparison principle. At the same time, the new conclusion of stability of these systems is more universal and contains the existing results. Finally, an example is given to illustrate the feasibility and validity of the obtained results.
文摘Many impulsive phenomena from physics, control theory, and economics urge us toinvestigate measure large scale systems. In this paper, the variation of parameters formulaof the large scale systems containing measures is established. By means of inequality methods and comparison theory, the stability, uniform stability, asymptotic stability, uniformasymptotic stability, and exponential stability properties of linear measure large scale systems are studied.
文摘This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula of large scale singular systems containing measures and delays is obtained.Employing inequality methods and comparison theory,the stability properties of large scale systems are studied.
文摘In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.
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.