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Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. (English) Zbl 1160.37439
Summary: In this letter, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

MSC:
37N99 Applications of dynamical systems
92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence
Software:
LMI toolbox; Matlab
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