By decomposing the state matrix into a symmetric part and an antisymmetric part, this paper investigates stability of continuous-time fractional positive systems, sufficient necessary condition for systems to be bounded in given interval is obtained. The results show that when system corresponding its asymptotically stable, also stable.

We consider the problem of decomposing an observed input matrix (or vector sequence) into the product of a mixing matrix with a component matrix , i.e. , where (a) the elements of the mixing matrix and the component matrix are non-negative, and (b) the underlying components are considered to be observations from an independent source. This is therefore a problem of non-negative independent comp...

We investigate the robust PCA problem of decomposing an observed matrix into the sum of a low-rank and a sparse error matrices via convex programming Principal Component Pursuit (PCP). In contrast to previous studies that assume the support of the error matrix is generated by uniform Bernoulli sampling, we allow non-uniform sampling, i.e., entries of the low-rank matrix are corrupted by errors ...

We consider the problem of decomposing an observed input matrix (or vector sequence) into the product of a mixing matrix with a component matrix , i.e. , where (a) the elements of the mixing matrix and the component matrix are non-negative, and (b) the underlying components are considered to be observations from an independent source. This is therefore a problem of non-negative independent comp...

This article is an extension of work which suggests using formal concepts as optimal factors of Factor Analysis. They discussed a method for decomposing a p × q binary matrix W into the Boolean matrix product P ◦ Q of a p × n binary matrix P and a n × q binary matrix Q with n as small as possible. We have generalised this factorization problem to the triadic case, looking for a decomposition of...

A heuristic for decomposing traffic matrices in TDMA satellite communication. With the time-division multiple access (TDMA) technique in satellite communication the problem arises to decompose a given n x n tramc matrix into a weighted sum of a small number of permutation matrices such that the sum of the weights becomes minimal. There are polynomial algorithms when the number of permutation ma...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n×d matrix W and a nonnegative d×m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others. A longstanding open question, posed by Cohen an...

A scaling of a nonnegative matrix A is a matrix XA Y -I. where X and Yare nonsingular. nonnegative diagonal matrices. Some condition may be imposed on the scaling, for exa'mple. when A is square, X = Y or det X = det Y. We characterize matrices for ' which there exists a scaling that satisfies predetermined upper and lower bound. Our principal tools are a piecewise linear theorem of the alterna...