Robust stability of switched Boolean networks with function perturbation. (English) Zbl 1500.92037
Summary: In genetic regulatory networks, gene mutations are one of natural phenomena, which attract much attention by biological researchers. In modeling gene networks using switched Boolean networks (SBNs), gene mutations can be described by function perturbations, which is a meaningful issue in analyzing function perturbation of SBNs. This paper studies robust stability of SBNs with function perturbation. With the help of semi-tensor product (STP) of matrices, one equivalent algebraic form of SBNs is established. By constructing two state sets, a criterion for global stability of SBNs under arbitrary switching signals is proposed. In order to relax the conditions of global stability, pointwise stabilizability and consistent stabilizability of SBNs are further considered. Based on state reachable sets, several criteria are established for the proposed kinds of stability. Finally, the obtained results are verified by two examples and lac operon in the Escherichia coli, respectively.
MSC:
| 92C42 | Systems biology, networks |
| 93D09 | Robust stability |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C29 | Boolean control/observation systems |
| 93B70 | Networked control |
Keywords:
switched Boolean networks; semi-tensor product of matrices; algebraic state space representation; robust stability; function perturbationReferences:
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