Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients

An improved Lyapunov functional with application to stability of Cohen-Grossberg neural networks of neutral-type with multiple delays

The essential objective of this research article is to investigate stability issue of neutral-type Cohen-Grossberg neural networks involving multiple time delays in states of neurons and multiple neutral delays in time derivatives of states of neurons in the network. By exploiting a modified and improved version of a previously introduced Lyapunov functional, a new sufficient stability criterion is obtained for global asymptotic stability of Cohen-Grossberg neural networks of neutral-type possessing multiple delays. The proposed new stability condition does not involve the time and neutral delay parameters. The obtained stability criterion is totally dependent on the system elements of Cohen-Grossberg neural network model. Moreover, the validity of this novel global asymptotic stability condition may be tested by only checking simple appropriate algebraic equations established within the parameters of the considered neutral-type neural network. In addition, an instructive numerical example is presented to indicate the advantages of our proposed stability result over the existing literature results obtained for stability of various classes of neutral-type neural networks having multiple delays.

A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays

This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types.

An improved stability result for delayed Takagi-Sugeno fuzzy Cohen-Grossberg neural networks

This work proposes a novel and improved delay independent global asymptotic stability criterion for delayed Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg neural networks exploiting a suitable fuzzy-type Lyapunov functional in the presence of the nondecreasing activation functions having bounded slopes. The proposed stability criterion can be easily validated as it is completely expressed in terms of the system matrices of the fuzzy neural network model considered. It will be shown that the stability criterion obtained in this work for this type of fuzzy neural networks improves and generalizes some of the previously published stability results. A constructive numerical example is also given to support the proposed theoretical results.

Passivity analysis of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters

This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.