Partial stability and stabilisation of Boolean networks |
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| Authors: | Hong-Wei Chen Liang-Jie Sun |
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| Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua, China;3. Department of Mathematics, Zhejiang Normal University, Jinhua, China |
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| Abstract: | In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results. |
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| Keywords: | Boolean (control) network partial stability partial stabilisation state-feedback control semi-tensor product of matrices |
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