In this note we present a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v and establish a priori and a posteriori error estimates. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and carry out the resulting small exponential matr...

In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dep...

The implementation of exponential integrators requires the action of the matrix exponential and related functions of a large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with others from the literature. As we are interested in ex...

In this paper, we introduce a new time series model having stochastic exponential tail. This is constructed based on the Normal Tempered Stable distribution with time-varying parameter. The captures tail, which generates volatility smile effect and term structure in option pricing. Moreover, describes of volatility. We empirically show skewness kurtosis by applying to analyze S&P 500 index retu...

This paper deals with the problems of exponential admissibility and H∞ control for a class of continuous-time switched singular systems with time-varying delay. The H∞ controllers to be designed include both the state feedback SF and the static output feedback SOF . First, by using the average dwell time scheme, the piecewise Lyapunov function, and the free-weighting matrix technique, an expone...

This paper is concerned with the problem of exponential stability for a class of stochastic neural networks with Markovian switching and mode-dependent interval time-varying delays. A novel Lyapunov-Krasovskii functional is introduced with the idea of delay-partitioning, and a new exponential stability criterion is derived based on the new functional and free-weighting matrix method. This new c...