New results on state estimation and stability analysis based H_∞ control for multi-delay hybrid stochastic neural network

Abstract

This paper researches the stability and stabilisation problems of stochastic neural network with multiple time delays. As for time delay, neuron state delay is first introduced in this paper. The neuron state delay and the activation function delay are considered simultaneously, which improves system performance effectively. Due to that part of the state is unmeasurable, this paper designs an observer for the observation of state information. By constructing an appropriate Lyapunov–Krasovskii functional and employing a method of combining free weighting matrix and integral inequality, an observer-based stability criterion is obtained. The conservativeness of delay upper bound is reduced actively. At last, a controller is designed for the stochastic neural network. Numerical examples are given to prove the effectiveness of the results.

Keywords:

• $H_{\mathrm{\infty }}$ control
• linear matrix inequalities(LMIs)
• multiple time delays
• neural network
• state estimation
• stochastic system

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61573095].