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**Exponential synchronization of stochastic delayed discrete-time complex networks.**
*(English)*
Zbl 1172.92002

Summary: This paper is concerned with the problem of synchronization for stochastic discrete-time driven-response networks with time-varying delays. By employing the Lyapunov functional method combined with stochastic analysis as well as feedback control techniques, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab.

A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.

A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.

### MSC:

93D15 | Stabilization of systems by feedback |

90B15 | Stochastic network models in operations research |

93E15 | Stochastic stability in control theory |

### Keywords:

synchronization; discrete-time networks; stochastic disturbances; time-varying delay; feedback controller; exponential mean square stability
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\textit{J. Liang} et al., Nonlinear Dyn. 53, No. 1--2, 153--165 (2008; Zbl 1172.92002)

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