# Abstract:

This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments. And the developed method can well reduce the conservatism compared with the existing results. Finally, an illustrative numerical example is given to show the effectiveness of our proposed method.

# Keywords:

linear matrix inequality (LMI), neutral stochastic time-delay systems, delay decomposition approach, exponential stability

93D09, 93E03

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