Search

This paper investigates the stability of complex-valued neural networks (CVNNs) with semi-Markovian jump (sMJ) and generally uncertain transition rates. Each transition rate may be totally unknown or its estimate is determined. Firstly, two improved reciprocally convex inequalities (RCIs) and three less conservative integral inequalities are generalized to the complex-valued domain. Secondly, the existence and uniqueness of the addressed networks are proposed by the complex-valued homeomorphism theorem. Thirdly, by constructing a Lyapunov–Krasovskii functional (LKF), delay-dependent robust stability criteria of the CVNNs are obtained by utilizing the improved complex-valued RCIs and integral inequalities. Finally, simulations are presented to demonstrate the effectivenes and practicality of the established method. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability of fuzzy neural networks with time-varying and unbounded continuously distributed delays in mean square. Based on a new Lyapunov-Krasovskii functional, by effective combination of Jensen integral inequality with reciprocally convex and quadratic convex combination method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which are expressed in terms of linear matrix inequalities, can be easily verified via MATLAB software. The main advantage of the proposed criteria lies in its reduced conservatism by means of the time delay-decomposition technique and Wirtinger-based inequality. In addition to that, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over the existing literature. [ABSTRACT FROM AUTHOR]

The anti-synchronization control is investigated for a class of uncertain stochastic chaotic neural networks with both Markovian jump parameters and mixed delays. The mixed delays consists of discrete and distributed time-varying delays. First, by combining the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent criterion is established to guarantee the state variables of the discussed stochastic chaotic neural networks to be globally exponential anti-synchronized. Next, by utilizing a novel lemma and the Jensen integral inequality, a delay-dependent criterion is proposed to achieve the globally stochastic robust anti-synchronization. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of linear matrix inequalities, which can be solved numerically by employing the standard Matlab LMI toolbox package. Finally, two examples are proposed to demonstrate the effectiveness and usefulness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability of a kind of fuzzy cellular neural networks with mixed delays under impulsive perturbations. The mixed delays include constant delay in the leakage term (i.e., 'leakage delay'), time-varying delays, and continuously distributed delays. By using the quadratic convex combination method, reciprocal convex approach, Jensen integral inequality, and linear convex combination technique, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature. [ABSTRACT FROM AUTHOR]