Robust state estimation for discrete-time BAM neural networks with time-varying delay

A New Result on $H_{\infty }$ State Estimation of Delayed Static Neural Networks

This brief presents a new guaranteed performance state estimation criterion for delayed static neural networks. To facilitate the use of the slope information about activation function, the estimation error of activation function is separated into two parts for the first time. Then, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which has fully captured the slope information of the activation. Based on the new LKF, a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with performance. The desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem. The simulation results show that the proposed method has much better performance than the most recent results.

Pinning Impulsive Synchronization of Reaction-Diffusion Neural Networks With Time-Varying Delays

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.

H∞ State Estimation for Discrete-Time Delayed Systems of the Neural Network Type With Multiple Missing Measurements

This paper investigates the H∞ state estimation problem for a class of discrete-time nonlinear systems of the neural network type with random time-varying delays and multiple missing measurements. These nonlinear systems include recurrent neural networks, complex network systems, Lur'e systems, and so on which can be described by a unified model consisting of a linear dynamic system and a static nonlinear operator. The missing phenomenon commonly existing in measurements is assumed to occur randomly by introducing mutually individual random variables satisfying certain kind of probability distribution. Throughout this paper, first a Luenberger-like estimator based on the imperfect output data is constructed to obtain the immeasurable system states. Then, by virtue of Lyapunov stability theory and stochastic method, the H∞ performance of the estimation error dynamical system (augmented system) is analyzed. Based on the analysis, the H∞ estimator gains are deduced such that the augmented system is globally mean square stable. In this paper, both the variation range and distribution probability of the time delay are incorporated into the control laws, which allows us to not only have more accurate models of the real physical systems, but also obtain less conservative results. Finally, three illustrative examples are provided to validate the proposed control laws.