| On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities |
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| 引用本文： | Min WU~1,Yong HE~(1,2),Jinhua SHE~3(1. School of Information Science and Engineering,Central South University,Changsha Hunan 410083,China,2. School of Mathematical Science and Computing Technology,Central South University,Changsha Hunan 410083,China,3. Department of Mechatronics,Tokyo University of Technology,Tokyo 192-0982,Japan). On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities[J]. 控制理论与应用(英文版), 2004, 2(2) |
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| 作者姓名： | Min WU~1 Yong HE~(1 2) Jinhua SHE~3(1. School of Information Science and Engineering Central South University Changsha Hunan 410083 China 2. School of Mathematical Science and Computing Technology Central South University Changsha Hunan 410083 China 3. Department of Mechatronics Tokyo University of Technology Tokyo 192-0982 Japan) |
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| 作者单位： | Min WU~1，Yong HE~(1，2)，Jinhua SHE~3(1. School of Information Science and Engineering，Central South University，Changsha Hunan 410083，China;2. School of Mathematical Science and Computing Technology，Central South University，Changsha Hunan 410083，China;3. Department of Mechatronics，Tokyo University of Technology，Tokyo 192-0982，Japan) |
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| 基金项目： | This work was supported by the Doctor Subject Foundation of China (No. 2000053303) |
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| 摘 要： | Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability of Lur'e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs), If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.
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On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities |
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| Min WU,Yong HE. On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities[J]. Journal of Control Theory and Applications, 2004, 2(2) |
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| Authors: | Min WU Yong HE |
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| Affiliation: | Min WU~1,Yong HE~ |
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| Abstract: | Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability of Lur'e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs), If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method. |
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| Keywords: | Lur'e control systems Absolute stability Robusmess Lyapunov function Linear matrix inequality |
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