Exponential Stabilization of Memristive Neural Networks via Saturating Sampled-Data Control

Abstract

This paper is concerned with the exponential stabilization of memristive neural networks (MNNs) by taking into account the sampled-data control and actuator saturation. On the one hand, the MNNs are converted into a tractable model by defining a class of logical switched functions. Based on this model, the connection weights of MNNs are dealt with by a robust analysis method. On the other hand, a saturating sampled-data controller containing an exponentially decaying term is designed. With the help of generalized sector condition and the Lyapunov stability theory, a novel sufficient condition ensuring the local exponential stability of the closed-loop systems is formulated in terms of linear matrix inequalities. In addition, three optimization problems are given to design the control gain with the aims of enlarging the sampling interval, expanding the estimation of the domain of attraction, and minimizing the size of actuators, while preserving the stability of the closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Analysis of Adaptive Synchronization for Stochastic Neutral-Type Memristive Neural Networks with Mixed Time-Varying Delays

“…Discrete Dynamics in Nature and Society So the conditions of Theorem 13 are satisfied, and we conclude that two coupled memristive neural networks (6) and (7) can be synchronized for almost every initial data. Now by taking the initial date as 푒(0) = [0.4, 0.5] , 퐾(0) = [10,15] and 휑 1 = 0.1, 휑 2 = 0.2, we can draw the dynamic curves of the error system, the evolution of adaptive coupling strength 푘 1 , 푘 2 , and the Brownian motion 휔(푡), respectively, as Figures 1-3.…”

“…In this section, the stochastic synchronization for the two coupled memristive neural networks (6) and (7) is investigated under Assumptions 1-6.…”

“…Therefore, applying LaSalle-type invariance principle (see [27,36]) for the stochastic differential delay equations, we can conclude that the coupled memristive neural networks (6) and (7) can be synchronized for almost every initial data. This completes the proof.…”

“…(6) and (7) with 퐷 = 0 can be synchronized for almost every initial data, if there exist positive diagonal matrices …”

“…In 2008, Hewlett-Packard research team [5] obtained a practical memristor device and exhibited its characteristic, such as nanoscale and the memory ability. It has been shown that memristors can be used to work as biological synapses in artificial neural network and replace resistor to simulate the human brain in memristor-based neural networks (MNNs) model, which would benefit many practical applications (see [6,7]). …”