Exponential stability of continuous-time and discrete-time cellular neural networks with delays
Applied Mathematics and Computation
Parameter-dependent robust stability of uncertain time-delay systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Finite state automata and simple recurrent networks
Neural Computation
A reference model approach to stability analysis of neural networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Neural Networks
Markovian architectural bias of recurrent neural networks
IEEE Transactions on Neural Networks
Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Information Sciences: an International Journal
IEEE Transactions on Neural Networks
IEEE Transactions on Signal Processing
New passivity analysis for neural networks with discrete and distributed delays
IEEE Transactions on Neural Networks
l2-l∞ filter design for discrete-time singular Markovian jump systems with time-varying delays
Information Sciences: an International Journal
Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays
Expert Systems with Applications: An International Journal
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Synchronization analysis of heterogeneous dynamical networks
Neurocomputing
pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching
Neural Processing Letters
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In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained.