Improved Stability Analysis Results of Generalized Neural Networks With Time-Varying Delays

Parametric Stability Criteria for Delayed Recurrent Neural Networks via Flexible Delay-Dividing Method

This article focuses on investigating the stability issue for recurrent neural networks (RNNs) with interval time-varying delays (TVDs) based on a flexible delay-dividing method with parameters, which are related to the delay derivative. First, an interval of delay is separated into parametric subintervals via the linear combination technique. Then, an establishment of Lyapunov-Krasovskii functional (LKF) is connected to the parameters, and a novel linear technology is suggested to dispose of integral terms in the derivatives of the constructed function. Finally, the validity and advantage of the inferred criteria are interpreted by the comparison of representative simulation examples.

Static pinning synchronization control of self-triggered coupling dynamical networks

In this paper, a new static pinning intermittent control based on resource awareness triggering is proposed. A multi-layer control technique is used to synchronize the coupled neural network. First, a hierarchical network structure including pinned and interaction layers is induced using each pinning strategy. Second, using the ideas of average aperiodic intermittent control (AIC) rate method and constructing an auxiliary function, a new lemma is proposed for the pinning intermittent synchronization of coupled networks, where the upper/lower bound restrictions on each control width for AIC are relaxed. Third, to obtain the desired synchronization behavior, a self-triggering mechanism (STM) is proposed to execute the AIC of the pinned and interaction layers. Moreover, the proposed STM is effective for the actuation of the static pinning impulsive control. The static pinning method modifies the single pinning and switching pinning impulsive control. Finally, the proposed results are applied to Chua's circuits, oscillators and small-world networks. Experimental results show the performance of the proposed STM which reduces 34.58% the number of control updates compared to a periodically intermittent event-triggered scheme. Further, for large-scale coupled networks, the N-dimensional Laplacian matrix LV can be decomposed into sp×sp and N-sp×N-sp dimensions by hierarchical method, thus reducing the complexity of calculation.

Hierarchical Stability Conditions for Two Types of Time-Varying Delay Generalized Neural Networks

In this article, the stability analysis for generalized neural networks (GNNs) with a time-varying delay is investigated. About the delay, the differential has only an upper boundary or cannot be obtained. For the both two types of delayed GNNs, up to now, the second-order integral inequalities have been the highest-order integral inequalities utilized to derive the stability conditions. To establish the stability conditions on the basis of the high-order integral inequalities, two challenging issues are required to be resolved. One is the formulation of the Lyapunov-Krasovskii functional (LKF), the other is the high-degree polynomial negative conditions (NCs). By transforming the integrals in N-order generalized free-matrix-based integral inequalities (GFIIs) into the multiple integrals, the hierarchical LKFs are constructed by adopting these multiple integrals. Then, the novel modified matrix polynomial NCs are presented for the 2N-1 degree delay polynomials in the LKF differentials. Thus, the hierarchical linear matrix inequalities (LMIs) are set up and the nonlinear problems caused by the GFIIs are solved at the same time. Eventually, the superiority of the provided hierarchical stability criteria is demonstrated by several numeric examples.