Abstract
This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form ofM-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results.
Highlights
Cellular neural networks (CNNs), initially proposed by Chua and Yang in 1988 [1], have been extensively investigated owing to their important applications in many areas such as image processing, pattern recognition, and combinatorial optimization
In order to take this vagueness into consideration, the fuzzy cellular neural networks (FCNNs) were proposed by Yang et al in [2, 3], which integrate fuzzy logic into the structure of traditional CNNs and maintain local connectedness among cells
The dynamics analysis problem of FCNNs has received an increasing research attention and some relevant results have been reported in the literature [4,5,6,7,8,9]
Summary
Cellular neural networks (CNNs), initially proposed by Chua and Yang in 1988 [1], have been extensively investigated owing to their important applications in many areas such as image processing, pattern recognition, and combinatorial optimization. Li and Wang [19] further discussed the existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses. We note that the results in the form of linear matrix inequalities (LMIs) are less conservative because they include suitable number of unknown parameters, and consider the excitatory and inhibitory effects of neuron on neural networks. To the best of our knowledge, the state estimation problem for discrete-time fuzzy cellular neural networks has not been investigated in the existing literatures, which elicits our research work. It is noted that the effects of neuron excitatory and inhibitory responses on neural networks are taken into account in the proposed approach, which will lead to less conservative results These conditions obtained are in the form of LMIs whose solution can be calculated by using MATLAB LMI toolbox
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