SCIENCE CHINA Information Sciences, Volume 63 , Issue 11 : 212201(2020) https://doi.org/10.1007/s11432-019-2664-7

Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control

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  • ReceivedJun 11, 2019
  • AcceptedSep 2, 2019
  • PublishedOct 9, 2020


This paper studies the stabilization problem of delayed memristive neural networks under event-triggered control. A refined switching event-trigger scheme that switches between variable sampling and continuous event-trigger can be designed by introducing an exponential decay term into the threshold function. Compared with the existing mechanisms, the proposed scheme can enlarge the interval between two successively triggered events and therefore can reduce the amount of triggering times. By constructing a time-dependent and piecewise-defined Lyapunov functional, a less-conservative criterion can be derived to ensure global stability of the closed-loop system. Based on matrix decomposition, equivalent conditions in linear matrix inequalities form of the above stability criterion can be established for the co-design of both the trigger matrix and the feedback gain. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and the advantages of the refined switching event-trigger scheme.


This work was supported by National Natural Science Foundation of China (Grant Nos. 61973199, 61473178, 61573008). We would thank anonymous reviewers for their valuable suggestions.


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  • Figure 1

    (Color online) The chaotic attractor of system (1) with initial conditions $(~-1.3,0.8)~^{\rm~T}$.

  • Table 1  

    Table 1Comparison of triggering times $t_{s}$ for RSETC and SETC schemes at $\tilde{h}_{k}~=~0.06$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    SETC [33-35] $\alpha~=0$, $\beta~=1$ $130$ $100$
    RSETC $\alpha~=0.01$, $\beta~=1$ $55$ $42$
    RSETC $\alpha~=0.1$, $\beta~=1$ $44$ $33$
  • Table 2  

    Table 2Comparison of triggering times $t_{s}$ for different $\beta$ at $\tilde{h}_{k}~=~0.06$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    RSETC $\alpha~=0.1$, $\beta~=5$ $127$ $100$
    RSETC $\alpha~=0.1$, $\beta~=2$ $93$ $73$
    RSETC $\alpha~=0.1$, $\beta~=1$ $44$ $34$
  • Table 3  

    Table 3Comparison of the triggering times $t_{s}$ between RSETC and SETC schemes at $\tilde{h}_{k}~=~0.014$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    SETC [33-35] $\alpha~=0,\beta=5$ $333$ $100$
    RSETC $\alpha~=0.001$, $\beta=5$ $235~$ $70~$
    RSETC $\alpha~=0.01$, $\beta=5$ $227~$ $68~$
  • Table 4  

    Table 4Comparison of triggering times $t_{s}$ for different $\beta$ at $\tilde{h}_{k}~=~0.014$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    RSETC $\alpha~=0.01$, $\beta=7$ $290$ $100$
    RSETC $\alpha~=0.01$, $\beta=5$ $227~$ $78~$
    RSETC $\alpha~=0.01$, $\beta=3$ $170~$ $58~$

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