L∞-gain analysis for positive systems with distributed delays

• Published in: Automatica (Oxford) Vol. 50; no. 1; pp. 175 - 179
• Main Authors: Shen, Jun, Lam, James
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2014; Elsevier
• 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; 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
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2013.09.037

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.