 On ℓ and gains for positive systems with bounded time-varying delaysJun Shen and James Lam International Journal of Systems Science, 2015, vol. 46, issue 11, 1953-1960 Abstract: This paper is devoted to the analysis of the ℓ∞ and L∞ gains for positive linear systems with interval time-varying delays. Through exploiting the monotonicity of the state trajectory, we first prove that for positive systems with constant delays, the ℓ∞ and L∞ gains are fully governed by the system matrices but independent of the delay size. Moreover, for positive systems with bounded time-varying delays, by comparing with the nominal systems with constant delays, it turns out that the ℓ∞ and L∞ gains are exactly the same as that of the constant delay systems. The results in this paper reveal that the ℓ∞ and L∞ gains of positive linear systems are not sensitive to the magnitude of time delays and hence the computation of ℓ∞ and L∞ gains of positive systems with bounded time-varying delays can be reduced to computing the ℓ∞ and L∞ gains of the corresponding delay-free systems. Both continuous-time and discrete-time cases are considered in this paper. Date: 2015 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:tsysxx:v:46:y:2015:i:11:p:1953-1960 Ordering information: This journal article can be ordered from DOI: 10.1080/00207721.2013.843217 Access Statistics for this article International Journal of Systems Science is currently edited by Visakan Kadirkamanathan More articles in International Journal of Systems Science from Taylor & Francis Journals |
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