Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems.

*(English)*Zbl 1293.93647Summary: This paper concerns the stability analysis problem for stochastic delayed switched Genetic Regulatory Networks (GRNs) with both stable and unstable subsystems. By employing the piecewise Lyapunov functional method combined with the average dwell time approach, we show that if the average dwell time is chosen sufficiently large and the derivative of the Lyapunov-like function for unstable subsystems is bounded by certain kind of continuous function, then exponential stability criteria of a desired degree are guaranteed. The derived results show that the minimal average dwell time is proportional to the time delays. Finally, an example is given to illustrate the effectiveness of the derived results.

##### MSC:

93D20 | Asymptotic stability in control theory |

90B15 | Stochastic network models in operations research |

93D30 | Lyapunov and storage functions |

93E15 | Stochastic stability in control theory |

##### Keywords:

exponential stability; switched genetic regulatory networks; stable and unstable subsystems; stochastic delayed switched genetic regulatory networks (GRNs); piecewise Lyapunov functional
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\textit{W. Zhang} et al., J. Franklin Inst. 350, No. 8, 2322--2333 (2013; Zbl 1293.93647)

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