Generalized cluster synchronization of Boolean control networks with delays in both the states and the inputs. (English) Zbl 1480.93401
Summary: In this paper, we study the generalized cluster synchronization problem for the Boolean control networks (BCNs) with delays in both the states and the inputs. First, by using the method of semi-tensor product of matrices, the original network is transformed into an equivalent extended system. Next, based on the updated iterative equation of the system, two types of generalized cluster synchronization are investigated: 1) generalized internal cluster synchronization within the BCN, and 2) generalized cluster synchronization between the BCN and the target reference network. Some necessary and sufficient conditions are proposed guaranteeing the realization of the generalized cluster synchronization. What is more, the gain matrices of the state-feedback controllers are explicitly designed. Numerical simulations are also given to illustrate effectiveness of the theoretical results obtained.
MSC:
| 93D99 | Stability of control systems |
| 93C29 | Boolean control/observation systems |
| 93B70 | Networked control |
| 93B52 | Feedback control |
Keywords:
generalized cluster synchronization; Boolean control networks; semi-tensor product of matrices; state-feedback controllersReferences:
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