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Zbl 1194.62109
Balasubramaniam, P.; Lakshmanan, S.; Jeeva sathya theesar, S.
State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. (English)
[J] Nonlinear Dyn. 60, No. 4, 661-675 (2010). ISSN 0924-090X; ISSN 1573-269X/e

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 2000:: *62M45 Neural nets and related approaches
60J75 Jump processes
15A39 Linear inequalities

Keywords: delay/interval-dependent stability; linear matrix inequality; Lyapunov-Krasovskii functional; Markovian jumping parameters; neural networks

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