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Novel delay-partitioning approaches to stability analysis for uncertain Lur’e systems with time-varying delays
Authors:Liang-Dong Guo  Sheng-Juan Huang  Li-Bing Wu
Institution:1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education and School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Huatian Engineering & Technology Corporation, MCC, Ma’anshan 243005, China;3. School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China;1. College of Science, Hebei Agricultural University, Baoding 071001, China;2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;3. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;4. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China;1. Graduate School of Mechanical and Aerospace Engineering, Gyeongsang National University, 501 Jinjudaero, Jinju 52828, Republic of Korea;2. Department of Electrical Engineering, Hanyang University, 222 Wangsimniro, Seoul 04763, Republic of Korea;1. Building 35B, Harbin Engineering University, Harbin, China;2. Ingkarni Wardli Building, North Terrace campus, The University of Adelaide, Adelaide, Australia;3. Building 61, Harbin Engineering University, Harbin, China;1. School of Automation, China University of Geosciences, Wuhan 430074, China;2. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China
Abstract:This work deals with the problem of absolute stability analysis for a class of uncertain Lur’e systems with time-varying delays. Novel delay-partitioning approaches are presented, which are dividing the variation interval of the delay into three subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on each of the obtained subintervals which can efficiently make use of the information of the delay and relate to the reciprocally convex combination technique and the Wirtinger-based integral inequality method. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). The merit of the proposed criteria lies in their less conservativeness and lower numerical complexity than relative literature. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.
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