This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involvi...By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.展开更多
This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are est...This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are established by using the Leray-Schauder alternative. An example is given to illustrate the results.展开更多
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金The project supported by the National Natural Science Foundation of China under the Grant of 59625511
文摘By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.
基金Supported by NSFC10271044, NSF2003kj005zd from Anhui Province Education Department, Talent Fund 05025104 of Anhui Province Education Department and Innovation Group Fund of Anhui University.
文摘This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are established by using the Leray-Schauder alternative. An example is given to illustrate the results.
