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Delay-range dependent stability criteria for neural networks with Markovian jumping parameters. (English) Zbl 1175.93206

Summary: The paper is concerned with a stability analysis problem for neural networks with Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrix \(P_i\) is introduced in this paper. The discrete delays are assumed to be time-varying and 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, a numerical example is provided to demonstrate the lower conservatism and the effectiveness of the proposed LMI conditions.

MSC:

93D99 Stability of control systems
92B20 Neural networks for/in biological studies, artificial life and related topics
60J75 Jump processes (MSC2010)
15A39 Linear inequalities of matrices
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