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Exponential synchronization of switched genetic oscillators with time-varying delays. (English) Zbl 1294.93009

Summary: 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.

MSC:

93A14 Decentralized systems
93D30 Lyapunov and storage functions
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