Two novel general summation inequalities to discrete-time systems with time-varying delay |
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Authors: | Jun Chen Shengyuan Xu Qian Ma Yongmin Li Yuming Chu Zhengqiang Zhang |
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Institution: | 1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;2. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou 221116, China;3. School of Science, Huzhou Teachers College, Huzhou 313000, Zhejiang, China;4. School of Electrical Engineering and Automation, Qufu Normal University, Rizhao 276826, China |
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Abstract: | This paper presents two novel general summation inequalities, respectively, in the upper and lower discrete regions. Thanks to the orthogonal polynomials defined in different inner spaces, various concrete single/multiple summation inequalities are obtained from the two general summation inequalities, which include almost all of the existing summation inequalities, e.g., the Jensen, the Wirtinger-based and the auxiliary function-based summation inequalities. Based on the new summation inequalities, a less conservative stability condition is derived for discrete-time systems with time-varying delay. Numerical examples are given to show the effectiveness of the proposed approach. |
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Keywords: | Corresponding author |
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