Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense

In this brief, by employing an improved Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique with the convex one, a new sufficient condition is derived to guarantee a class of delayed neural networks (DNNs) to be globally asymptotically stable. Since some previously ignored terms can be considered during the estimation of the derivative of LKF, a less conservative stability criterion is derived in the forms of linear matrix inequalities, whose solvability heavily depends on the information of addressed DNNs. Finally, we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods.

Combined Convex Technique on Delay-Dependent Stability for Delayed Neural Networks

This paper focuses on the problem of delay-dependent stability and dissipativity analysis of generalized neural networks (GNNs) with Markovian jump parameters and two delay components. By constructing novel augmented Lyapunov–Krasovskii functional (LKF), using free-matrix-based inequality to estimate the derivative of Lyapunov function and employing the reciprocally convex approach to consider the relationship between the time-varying delay and its interval, some improved delay-dependent stability criteria and dissipativity criteria are established in terms of linear matrix inequalities. Moreover, the obtained criteria is extended to analyze the stability analysis of GNNs with two delay components and the passivity analysis of GNNs with one delay. Numerical examples are given to show the effectiveness and the significant improvement of the proposed methods.

Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components

Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays

http://pris.bit.edu.cn/docs/2014-03/20140312111957316370.pdf

Stability analysis of static recurrent neural networks with interval time-varying delay

This paper investigates robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional (LKF), some inequality techniques and stochastic stability theory, new delay-dependent stability criteria have been obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results.

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters ☆

The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov–Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.

A. Manivannan

Papers

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters ☆

Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks☆

Dynamical analysis of antigen-driven T-cell infection model with multiple delays

Robust stability criteria for uncertain neutral type stochastic system with Takagi-Sugeno fuzzy model and Markovian jumping parameters