Stabilization of Boolean control networks with stochastic impulses |
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| Institution: | 1. School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China;2. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;3. School of Mathematics, Southeast University, Nanjing 210096, China;1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. Institute of Data Science and Technology, Shandong Normal University, Jinan 250014, PR China;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results. |
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