Abstract
In this paper, the exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with random delay and Markovian switching. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed recurrent neural network with Markovian switching is exponentially stable. The analysis is based on the Lyapunov-Krasovskii functional and stochastic analysis approach, and the conditions are expressed in terms of linear matrix inequalities, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.
Highlights
In recent years, the neural networks NNs have been extensively studied because of their immense application potentials, such as signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization
The exponential stability analysis problem is considered for a class of recurrent neural networks RNNs with random delay and Markovian switching
Motivated by the above discussions, the aim of this paper is to investigate the exponential stability of RNNs with random delay and Markovian switching in mean square
Summary
The neural networks NNs have been extensively studied because of their immense application potentials, such as signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization. The stability problem of delayed neural networks has become a topic of great theoretic and practical importance. In a PULN, the output signal of the node is transferred to another node by multibranches with arbitrary time delay which is random and its probabilistic characteristic can often be measured by the statistical methods. For this case, if some values of the time delay are very large but the probabilities of the delay taking such large values are very small, it may result in a more conservative result if only the information of variation range of the time delay is considered. The discrete values of the delay may correspond to “low”, “medium”, and “high” network loads
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