Exponential synchronization of switched genetic oscillators with time-varying delays |
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| Authors: | Xiongbo Wan Li Xu Huajing Fang Fang Yang Xuan Li |
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| Institution: | 1. College of Engineering, Huazhong Agricultural University, Wuhan 430070, China;2. Department of Electronics and Information Systems, Akita Prefectural University, 84-4 Tsuchiya-Ebinokuchi, Honjo, Akita 015-0055, Japan;3. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | This paper addresses the problem of exponential synchronization of switched genetic oscillators with time-varying delays. Switching parameters and three types of nonidentical time-varying delays, that is, the self-delay, the intercellular coupling delay, and the regulatory delay are taken into consideration in genetic oscillators. By utilizing the Kronecker product techniques and ‘delay-partition’ approach, a new Lyapunov–Krasovskii functional is proposed. Then, based on the average dwell time approach, Jensen?s integral inequality, and free-weighting matrix method, delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). These conditions guarantee the exponential synchronization of switched genetic oscillators with time-varying delays whose upper bounds of derivatives are known and unknown, respectively. A numerical example is presented to demonstrate the effectiveness of our results. |
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