L∞-gain analysis for positive systems with distributed delays
This paper addresses the L∞-gain analysis problem of positive linear systems with distributed delays. By virtue of the positivity and linearity of the system, we first study the monotonic and asymptotic property of the system with distributed delays. Then, by resorting to an auxiliary system without...
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| Published in | Automatica (Oxford) Vol. 50; no. 1; pp. 175 - 179 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.01.2014
Elsevier |
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| Abstract | This paper addresses the L∞-gain analysis problem of positive linear systems with distributed delays. By virtue of the positivity and linearity of the system, we first study the monotonic and asymptotic property of the system with distributed delays. Then, by resorting to an auxiliary system without time delay, an explicit expression of the L∞-gain of positive systems with distributed delays is given in terms of system matrices. Moreover, the results are extended to positive systems with distributed delays over a bounded time-varying interval. Finally, a necessary and sufficient condition on the L∞-gain of an asymptotically stable positive system with distributed delays is presented via linear programming. |
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| AbstractList | This paper addresses the L∞-gain analysis problem of positive linear systems with distributed delays. By virtue of the positivity and linearity of the system, we first study the monotonic and asymptotic property of the system with distributed delays. Then, by resorting to an auxiliary system without time delay, an explicit expression of the L∞-gain of positive systems with distributed delays is given in terms of system matrices. Moreover, the results are extended to positive systems with distributed delays over a bounded time-varying interval. Finally, a necessary and sufficient condition on the L∞-gain of an asymptotically stable positive system with distributed delays is presented via linear programming. |
| Author | Shen, Jun Lam, James |
| Author_xml | – sequence: 1 givenname: Jun surname: Shen fullname: Shen, Jun email: junshen2009@gmail.com – sequence: 2 givenname: James surname: Lam fullname: Lam, James email: james.lam@hku.hk |
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| Keywords | L∞-gain Time-delay systems Positive systems Distributed delays Necessary and sufficient condition Positivity Linear programming Delay system Distributed system Positive system L Modeling Interval arithmetic Bounded delay Distributed delay gain Asymptotic stability Linear system Linearity Delay time Asymptotic approximation System analysis Time complexity |
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| Snippet | This paper addresses the L∞-gain analysis problem of positive linear systems with distributed delays. By virtue of the positivity and linearity of the system,... |
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| SubjectTerms | [formula omitted]-gain Applied sciences Computer science; control theory; systems Control system analysis Control theory. Systems Distributed delays Exact sciences and technology Positive systems System theory Time-delay systems |
| Title | L∞-gain analysis for positive systems with distributed delays |
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