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Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties
Institution:1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. The Department of Electrical and Computer Engineering, The University of Auckland, Private Bag, 92019 Auckland, New Zealand;3. Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;4. School of Life Sciences and Technology, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;1. School of Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel;2. Department of Mechanical Engineering, Technion, Haifa 32000, Israel;1. University of Novi Sad, Faculty of Sciences, Department of Physics, Trg Dositeja Obradovića 4, 21000 Novi Sad, Vojvodina, Serbia;2. Academy of Criminalistic and Police Studies, Cara Dušana 196, 11080 Zemun, Serbia;3. University of Novi Sad, Technical Faculty “M. Pupin”, Đure Đakovića bb, 23000 Zrenjanin, Vojvodina, Serbia;4. Academy of Sciences and Arts of the Republic of Srpska, Bana Lazarevića 1, 78000 Banja Luka, Bosnia and Herzegovina;1. Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 310036, China;2. Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;3. Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610051, China;4. Department of Psychology, University of Graz, Graz 8010, Austria;5. The Research Center for Complex System Science, University of Shanghai for Science and Technology, Shanghai 200093, China;1. School of Mechanical Engineering, Yeungnam University, Kyongsan 712-749, South Korea;2. Collective Dynamics of Complex Systems Research Group, Binghamton University, State University of New York, Binghamton, NY 13902-6000, USA
Abstract:This study examines the problem of robust stability of uncertain stochastic genetic regulatory networks with time-varying delays. The system’s uncertainties are modeled as both polytopic form and structured linear fractional form. Based on a novel augmented Lyapunov–Krasovskii functional and different integral approaches, new stability conditions have been derived. Furthermore, these stability criteria can be applicable to both fast and slow time-varying delays. Finally, a numerical example is presented to illustrate the effectiveness of the proposed stability conditions.
Keywords:Genetic regulatory network  Lyapunov–Krasovskii functional  Linear matrix inequality  Polytopic uncertainty  Linear fractional parametric uncertainty
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