Abstract
We aim to further study the global stability of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). According to our previous work, it is known that a BCN under ASDC can be transformed into a switched Boolean network (SBN), and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN. Unfortunately, since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems, the SBN considered has at least one stable subsystem. The central thought in this paper is that switching behavior also has good stabilization; i.e., the SBN can also be stable with appropriate switching laws designed, even if all subsystems are unstable. This is completely different from that in our previous work. Specifically, for this case, the dwell time (DT) should be limited within a pair of upper and lower bounds. By means of the discretized Lyapunov function and DT, a sufficient condition for global stability is obtained. Finally, the above results are demonstrated by a biological example.
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Liang-jie SUN, Jian-quan LU, and Wai-Ki CHING declare that they have no conflict of interest.
Project supported by the Natural Science Foundation of Jiangsu Province, China (No. BK20170019), the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China (Nos. 61973078, 61573102, and 11671158), Hong Kong RGC GRF, China (No. 17301519), and IMR and RAE Research Fund from Faculty of Science, HKU, China
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Sun, Lj., Lu, Jq. & Ching, WK. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable. Front Inform Technol Electron Eng 21, 260–267 (2020). https://doi.org/10.1631/FITEE.1900312
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DOI: https://doi.org/10.1631/FITEE.1900312
Key words
- Aperiodic sampled-data control
- Boolean control networks
- Unstable subsystem
- Discretized Lyapunov function
- Dwell time