This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.

In this paper, we analyze the exponential stability, passivity, and (Q, G, R)-γ-dissipativity of generalized neural networks (GNNs) including mixed time-varying delays in state vectors. Novel exponential stability, passivity, and (Q, G, R)-γ-dissipativity criteria are developed in the form of linear matrix inequalities for continuous-time GNNs by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and applying a new weighted integral inequality for handling integral terms in the time derivative of the established LKF for both single and double integrals. Some special cases are also discussed. The superiority of employing the method presented in this paper over some existing methods is verified by numerical examples.

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.