This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is trans...This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
