On Global Dissipativity of Nonautonomous Neural Networks With Multiple Proportional Delays

This brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays. By using a novel constructive approach based on some comparison techniques for differential inequalities, new explicit delay-independent conditions are derived using M-matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system. The method presented in this brief is also utilized to derive a generalized exponential estimate for a class of Halanay-type inequalities with proportional delays. Finally, three numerical examples are given to illustrate the effectiveness and improvement of the obtained results.

Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying delays

In this paper, we study the finite-time synchronization problem for recurrent neural networks with discontinuous activations and time-varying delays. Based on the finite-time convergence theory and by using the nonsmooth analysis technique, some finite-time synchronization criteria for the considered neural network model are established, which are new and complement some existing ones. The feasibility and effectiveness of the proposed synchronization method are supported by two examples with numerical simulations.

Global robust dissipativity of interval recurrent neural networks with time-varying delay and discontinuous activations

In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations.

Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay

This paper is concerned with the state estimation problem for a class of discrete-time stochastic neural networks (DSNNs) with random delays. The effect of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By employing a Lyapunov-Krasovskii functional, sufficient delay-distribution-dependent conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimator which can be checked readily by the Matlab toolbox. The main feature of the results obtained in this paper is that they are dependent on not only the bound but also the distribution probability of the time delay, and we obtain a larger allowance variation range of the delay, hence our results are less conservative than the traditional delay-independent ones. One example is given to illustrate the effectiveness of the proposed result.