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Stability theory and a linear matrix inequality (LMI) approach are developed to establish sufficient conditions for the NNs to be globally asymptotically stable and to design a state estimator for the discrete-time neural networks. Both the discrete delay and distribute delays employ decomposing the delay interval approach, and the Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals, such that a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.<\/jats:p>","DOI":"10.1155\/2014\/209486","type":"journal-article","created":{"date-parts":[[2014,2,18]],"date-time":"2014-02-18T16:01:17Z","timestamp":1392739277000},"page":"1-14","source":"Crossref","is-referenced-by-count":1,"title":["State Estimation for Discrete-Time Stochastic Neural Networks with Mixed Delays"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9082-9554","authenticated-orcid":true,"given":"Liyuan","family":"Hou","sequence":"first","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 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