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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 11464-11481. doi: 10.3934/mbe.2023508
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Survey of semi-tensor product method in robustness analysis on finite systems

  • School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

  • Academic Editor: Yang Kuang
  • Received: 02 February 2023 Revised: 23 March 2023 Accepted: 31 March 2023 Published: 28 April 2023

  • Recently, the theory of semi-tensor product (STP) method of matrices has received much attention from variety communities covering engineering, economics and industries, etc. This paper describes a detailed survey on some recent applications of the STP method in finite systems. First, some useful mathematical tools on the STP method are provided. Second, many recent developments about robustness analysis on the given finite systems are delineated, such as robust stable analysis of switched logical networks with time-delayed, robust set stabilization of Boolean control networks, event-triggered controller design for robust set stabilization of logical networks, stability analysis in distribution of probabilistic Boolean networks, and how to solve a disturbance decoupling problem by event triggered control for logical control networks. Finally, several research problems in future works are predicted.

    Citation: Guodong Zhao, Haitao Li, Ting Hou. Survey of semi-tensor product method in robustness analysis on finite systems[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 11464-11481. doi: 10.3934/mbe.2023508

    Related Papers:

  • Recently, the theory of semi-tensor product (STP) method of matrices has received much attention from variety communities covering engineering, economics and industries, etc. This paper describes a detailed survey on some recent applications of the STP method in finite systems. First, some useful mathematical tools on the STP method are provided. Second, many recent developments about robustness analysis on the given finite systems are delineated, such as robust stable analysis of switched logical networks with time-delayed, robust set stabilization of Boolean control networks, event-triggered controller design for robust set stabilization of logical networks, stability analysis in distribution of probabilistic Boolean networks, and how to solve a disturbance decoupling problem by event triggered control for logical control networks. Finally, several research problems in future works are predicted.


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