In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant kernel. In this case it is not obvious how to take advantage of t...

Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear discriminant analysis (LDA). However, for data with high dimension, one has to solve a large matrix exponential eigenproblem in this method, and the time com...

Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing A e and for computing At e with many 0 t  re...

Stochastic models based on matrix exponential structures, like matrix exponential distributions and rational arrival processes, have gained popularity in analytical models recently. However the application of these models in simulation based evaluations is not as widespread yet. One of the possible reasons is the lack of efficient random variates generation methods. In this paper we propose met...

In this work is proposed a method using orthogonal matrix transform properties to encrypt and decrypt a message. It will be showed how to use matrix’s functions to create complex encryptions. Because orthogonal matrix are always diagonalizable on R, and the exponential of a diagonal matrix is easy to compute, the exponential of orthogonal matrix will be used to encrypt text messages.

⎯The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of th...

We propose a new analytic formula for evaluating the derivatives of a matrix exponential. In contrast to the diagonalization method, eigenvalues and eigenvectors do not appear explicitly in the derivation, although we show that a necessary and sufficient condition for the validity of the formula is that the matrix has distinct eigenvalues. The new formula expresses the derivatives of a matrix e...