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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Bibliographic Details
Published in:Automatica (Oxford) 2014-01, Vol.50 (1), p.175-179
Main Authors: Shen, Jun, Lam, James
Format: Article
Language:English
Subjects:
[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
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.09.037