Generalized cluster synchronization of Boolean control networks with delays in both the states and the inputs |
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| Affiliation: | 1. School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China;2. School of Mathematics, Southeast University, Nanjing 210096, China;3. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. Institute of Automation, Qufu Normal University, Qufu 273165, PR China;1. School of Mathematics, Southeast University, Nanjing 210096, China;2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. School of Information Engineering, Huzhou University, Huzhou 313000, China;4. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China;5. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. School of Information Science and Engineering, Shandong Normal University, Jinan 250014, PR China |
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| Abstract: | 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. |
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