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Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. (English) Zbl 1221.93254
Summary: This paper investigates delay-dependent robust exponential state estimation of Markovian jumping fuzzy neural networks with mixed random time-varying delay. In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the robust exponential state estimation of Markovian jumping Hopfield neural networks with mixed random time-varying delays. Moreover probabilistic delay satisfies a certain probability-distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. 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 exponentially stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay-dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally some numerical examples are provided to demonstrate the effectiveness of the proposed method.
##### MSC:
 93E10 Estimation and detection in stochastic control 34K50 Stochastic functional-differential equations 60J28 Applications of continuous-time Markov processes on discrete state spaces 82C32 Neural nets (statistical mechanics) 92B20 General theory of neural networks (mathematical biology)
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