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**State estimation for jumping recurrent neural networks with discrete and distributed delays.**
*(English)*
Zbl 1335.93125

Summary: This paper is concerned with the state estimation problem for a class of Markovian neural networks with discrete and distributed time-delays. 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 asymptotically stable in the mean square. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. Both the existence conditions and the explicit characterization of the desired estimator are derived. Furthermore, it is shown that the traditional stability analysis issue for delayed neural networks with Markovian jumping parameters can be included as a special case of our main results. Finally, numerical examples are given to illustrate the applicability of the proposed design method.

### MSC:

93E10 | Estimation and detection in stochastic control theory |

60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |

60J75 | Jump processes (MSC2010) |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

### Keywords:

neural networks; Markovian jumping systems; state estimation; time-delays; asymptotic stability; linear matrix inequalities### Software:

LMI toolbox### References:

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