Containment problem of finite-field networks with fixed and switching topology

作者：

Highlights：

• The containment problem is generalized to FFNs, which enriches the theory of FFNs and extends the application of STP.

• Using STP, we propose some new necessary and sufficient conditions to achieve containment by analyzing the property of structural matrix. The conditions listed in this paper are easily to check via the MATLAB toolbox.

• Comparison with the existing works: From the point of systems, the state variables in [14,16,17,20] is 1-dimensional, while the state variables in this paper is k-dimensional; From the point of research methods, the conventional matrix theory and graph theory are the main mathematical tool in [14–17,20], including characteristic polynomial, eigenvalue and connectivity, while the STP method is more convenient to check via MATLAB toolbox.

摘要

•The containment problem is generalized to FFNs, which enriches the theory of FFNs and extends the application of STP.•Using STP, we propose some new necessary and sufficient conditions to achieve containment by analyzing the property of structural matrix. The conditions listed in this paper are easily to check via the MATLAB toolbox.•Comparison with the existing works: From the point of systems, the state variables in [14,16,17,20] is 1-dimensional, while the state variables in this paper is k-dimensional; From the point of research methods, the conventional matrix theory and graph theory are the main mathematical tool in [14–17,20], including characteristic polynomial, eigenvalue and connectivity, while the STP method is more convenient to check via MATLAB toolbox.

论文关键词：Containment,Finite-field network,Set stability,Semi-tensor product of matrices,Switching topology

论文评审过程：Received 4 April 2021, Revised 14 June 2021, Accepted 8 July 2021, Available online 20 July 2021, Version of Record 20 July 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126519