Some augmented approaches to the improved stability criteria for linear systems with time-varying delays |
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| Institution: | 1. School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea;2. Center for Global Converging Humanities, Kyung Hee University, Yongin 17104, Republic of Korea;1. School of Electrical Engineering, Chungbuk National University, Cheongju, 28644, South Korea;2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India;3. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea;1. School of Artificial Intelligence, Shenyang University of Technology, Shenyang, Liaoning, 110870, China;2. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, China;1. School of Electrical Engineering, Chungbuk National University, Cheongju 28644, South Korea;2. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India;3. Department of Mathematics, Sungkyunkwan University, Suwon 440–746, South Korea;1. School of Electrical Engineering, Chungbuk National University, 1 Chungdae-ro, Cheongju 28644, Republic of Korea;2. Center for Global Converging Humanities, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin 17104, Republic of Korea;3. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India;1. Division of Electronic Engineering, Jeonbuk National University, 567 Baekje-daero, Jeonju 54896, Republic of Korea;2. Center for Global Conversing Humanities, Kyung Hee University, 1732 Deogyeong-daero, Yongin 17104, Republic of Korea;3. Department of Electrical Engineering, Yeungnam University, Gyongsan 38541, Republic of Korea |
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| Abstract: | This work investigates the improved stability conditions for linear systems with time-varying delays via various augmented approaches. Some augmented approaches are augmented Lyapunov-Krasovskii functionals, augmented zero equalities, and the augmented zero equality approach. At first, by constructing augmented Lyapunov-Krasovskii functionals including the state vectors which were not considered in the previous works and augmented zero equalities, a stability criterion is proposed in the forms of linear matrix inequalities. Through the proposed Lyapunov-Krasovskii functionals and an additional functional derived from the integral inequality, a slightly improved result is derived. The proposed results do not consider the increase in the computational complexity to achieve a larger delay bound. So, by applying the augmented zero equality approach, which is a method of grafting the proposed augmented zero equality proposed in Finsler Lemma, to the proposed result, an enhanced stability result was derived. Also, the computational complexity is reduced by appropriately adjusting any vector of the integral inequality utilized in the proposed criteria. By applying some numerical examples to the proposed conditions, the effectiveness and superiority of the results are confirmed. |
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