Abstract
This paper concerns the robust synchronization problems for discrete-time coupled neural networks with discrete time delay and distributed time delays. Inner parameters in individual neural network are subject to be uncertain and both coupled matrixes and weight matrixes are supposed to switch from one mode to another because of the markovian jumping chain. Mixed time delays contain discrete and distributed time delays and the mixed time delays not only exist in the individual neural cell, but also exist in the coupled cells. By using the novel Lyapunov-Krasovskii functional method and Kronecker product as tools, mean square stability conditions are provided in terms of linear matrix inequalities. In numerical simulations, two examples (with and without unknown parameters) are given and simulation results show the robustness and effectiveness of our methods.
Highlights
In the past decades, dynamical neural networks have been widely applied in a variety of areas, such as signal processing, image processing, pattern recognition, combinatorial optimization problems and so on
Dynamical properties with markovian jumping chain have been applied into the research of dynamical recurrent neural networks, complex dynamical networks and other complicated dynamical networks [14]–[18]
Based on the theorem 1, the discrete-time coupled neural networks with mixed time delays will get the synchronization and it is proved by numerical simulations
Summary
Dynamical neural networks have been widely applied in a variety of areas, such as signal processing, image processing, pattern recognition, combinatorial optimization problems and so on (see, for instance [1]–[5]). For a class of neural networks with finite states, markovian jumping chain is an effective tool to deal with the mode switching problems. H. Zhang et al.: Robust Synchronization for Discrete-Time Coupled Markovian Jumping Neural Networks time delays attract more and more researchers’ attentions. Some sufficient conditions for stability problems of discrete neural networks have been derived by some researchers, as far as we know, there has been no literatures investigate the synchronization problem for discrete-time coupled Markovian jumping neural networks with unknown parameters and mixed time-delays both in the inner neural cell and in the outer coupled neural cells. This paper considers the stability analysis and robust synchronization problems for a class of discrete-time coupled Markovian jumping neural networks with mixed time-delays. Matrices dimensions are assumed to be compatible for algebraic operations
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