Bounded Real Lemmas for Fractional Order Systems
This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relax...
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| Veröffentlicht in: | International journal of automation and computing 2015-04, Vol.12 (2), p.192-198 |
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| container_title | International journal of automation and computing |
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| creator | Liang, Shu Wei, Yi-Heng Pan, Jin-Wen Gao, Qing Wang, Yong |
| description | This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods. |
| doi_str_mv | 10.1007/s11633-014-0868-4 |
| format | Article |
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The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. 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J. Autom. Comput</addtitle><addtitle>国际自动化与计算杂志(英文版)</addtitle><description>This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. 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J. Autom. Comput</stitle><addtitle>国际自动化与计算杂志(英文版)</addtitle><date>2015-04-01</date><risdate>2015</risdate><volume>12</volume><issue>2</issue><spage>192</spage><epage>198</epage><pages>192-198</pages><issn>1476-8186</issn><issn>2153-182X</issn><eissn>1751-8520</eissn><eissn>2153-1838</eissn><abstract>This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. 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| subjects | bounded CAE) and Design Computation Computational efficiency Computer Applications Computer-Aided Engineering (CAD Control Control systems Controllers Engineering Fractional H-infinity control H∞control H∞norm inequality(LMI) lemmas linear Linear matrix inequalities L∞norm Mathematical analysis matrix Mechatronics Norms order real Regular Paper Robotics Synthesis systems Systems analysis Systems stability |
| title | Bounded Real Lemmas for Fractional Order Systems |
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