Search

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov-Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected. [ABSTRACT FROM AUTHOR]

This paper studies the Mittag-Leffler stability and synchronization of fractional neural networks with multi-delays (FNNMs). First, by using the weak additivity Eα(δt2α)Eα(δt1α)≤Eα(δ(t1+t2)α)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$E_\alpha (\delta t^\alpha _2)E_\alpha (\delta t_1^\alpha )\le E_\alpha (\delta (t_1+ t_2)^\alpha )$$\end{document} of the Mittag-Leffler function, the classical Halanay inequality is extended to a more comprehensive version cD0αr(t)≤κ(t)r(t)+χ(t)r(t-τ(t))+∫t-ρ(t)tG(t,s)r(s)ds+c(t)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^cD_0^\alpha r(t)\le \kappa (t)r(t)+\chi (t)r{(t-\tau (t))}+\int _{t-\rho (t)}^t{G(t,s)r(s)} \,\textrm{d} s+c(t)$$\end{document}, which is critical to the stability assessment research for fractional neural networks (FNNs). Based on the new inequality, a nonlinear matrix inequality (NMI) criterion for the Mittag-Leffler stability of FNNMs is derived. The nonlinear matrix criterion can be solved step by step with the linear matrix inequality (LMI) toolbox, thus avoiding the limitations of searching LMI criteria. In addition, a Mittag-Leffler synchronization criterion in terms of NMI is presented for master-salve FNNMs under an adaptive feedback controller. Finally, there are three numerical examples as a demonstration of the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability and passivity analysis for a class of discrete-time linear systems. A novel general free-matrix-based summation inequality is proposed, and two improved stability criteria in terms of linear matrix inequalities (LMIs) are derived by employing the new summation inequality. Furthermore, when an external disturbance appears, a sufficient condition is established to ensure the considered linear system to be passive. Three numerical examples are provided to demonstrate the improvement of the proposed method. [ABSTRACT FROM AUTHOR]