Local and global exponential synchronization of complex delayed dynamical networks with general topology
Jin-Liang Wang Zhi-Chun Yang Tingwen Huang Mingqing Xiao
In this paper, we consider a generalized complex network possessing general topology, in which the coupling may be nonlinear, time-varying, nonsymmetric and the elements of each node have different time-varying delays. Some criteria on local and global exponential synchronization are derived in form of linear matrix inequalities (LMIs) for the complex network by constructing suitable Lyapunov functionals. Our results show that the obtained sufficient conditions are less conservative than ones in previous publications. Finally, two numerical examples and their simulation results are given to illustrate the effectiveness of the derived results.
keywords: Complex networks time-varying delays exponential synchronization.
Realization of joint spectral radius via Ergodic theory
Xiongping Dai Yu Huang Mingqing Xiao
Based on the classic multiplicative ergodic theorem and the semi-uniform subadditive ergodic theorem, we show that there always exists at least one ergodic Borel probability measure such that the joint spectral radius of a finite set of square matrices of the same size can be realized almost everywhere with respect to this Borel probability measure. The existence of at least one ergodic Borel probability measure, in the context of the joint spectral radius problem, is obtained in a general setting.
keywords: random product of matrices joint spectral radius. The finiteness conjecture
On identifiability of 3-tensors of multilinear rank $(1,\ L_{r},\ L_{r})$
Ming Yang Dunren Che Wen Liu Zhao Kang Chong Peng Mingqing Xiao Qiang Cheng

In this paper, we study a specific big data model via multilinear rank tensor decompositions. The model approximates to a given tensor by the sum of multilinear rank $(1, \ L_{r}, \ L_{r})$ terms. And we characterize the identifiability property of this model from a geometric point of view. Our main results consists of exact identifiability and generic identifiability. The arguments of generic identifiability relies on the exact identifiability, which is in particular closely related to the well-known "trisecant lemma" in the context of algebraic geometry (see Proposition 2.6 in [1]). This connection discussed in this paper demonstrates a clear geometric picture of this model.

keywords: Multilinear algebra tensor rank generically unique multilinear rank big data algebraic geometry

Year of publication

Related Authors

Related Keywords

[Back to Top]