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State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. (English) Zbl 1194.62109
Summary: The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix ${P}_{i}$ is introduced in this paper. The discrete delay is assumed to be time-varying and to belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov-Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.
##### MSC:
 62M45 Neural nets and related approaches (inference from stochastic processes) 60J75 Jump processes 15A39 Linear inequalities of matrices
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