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State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. (English) Zbl 1268.92012
Summary: The state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameters based on passivity theory. 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 is globally stable in the mean square and passive from the control input to the output error. Based on a new Lyapunov-Krasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and results.
MSC:
92B20General theory of neural networks (mathematical biology)
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces
15A45Miscellaneous inequalities involving matrices
34K35Functional-differential equations connected with control problems
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