Observability of singular Boolean control networks with state delays |
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| Institution: | 1. School of Mathematics, Shandong University, Jinan 250100, Shandong, P. R. China;2. School of Management, Shandong University, Jinan 250100, Shandong, P. R. China;1. School of Mathematical Science, Liaocheng University, Liaocheng 252026, P.R. China;2. School of Science and Technology, University of Camerino, Camerino 62032, Italy |
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| Abstract: | This paper investigates the observability of singular Boolean control networks (SBCNs) with state delays. First, via Cheng product, the considered system is converted into its algebraic form. Then, under the uniqueness of the solution, two methods are proposed to transform the system into a general Boolean control network (BCN). Therefore, the considered system’s observability is equivalent to the BCN’s observability. Subsequently, the restricted input-state incidence matrix is introduced and some necessary and sufficient conditions are presented for the observability of BCNs with state delays. Finally, two illustrative examples are presented to show that the main results obtained are effective in analyzing the observability of SBCNs with state delays. |
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