Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities.

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.

Robust Stabilization of Delayed Neural Networks: Dissipativity-Learning Approach.

This paper examines the robust stabilization problem of continuous-time delayed neural networks via the dissipativity-learning approach. A new learning algorithm is established to guarantee the asymptotic stability as well as the (Q,S,R) - α -dissipativity of the considered neural networks. The developed result encompasses some existing results, such as H∞ and passivity performances, in a unified framework. With the introduction of a Lyapunov-Krasovskii functional together with the Legendre polynomial, a novel delay-dependent linear matrix inequality (LMI) condition and a learning algorithm for robust stabilization are presented. Demonstrative examples are given to show the usefulness of the established learning algorithm.

Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays.

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.