Exponential stability of homogeneous positive systems of degree one with time-varying delays

Hamid Reza Feyzmahdavian, Themistoklis Charalambous, Mikael Johansson

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

78 Sitaatiot (Scopus)

Abstrakti

While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This technical note presents a set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, when the time delays have a known upper bound, we derive necessary and sufficient conditions for exponential stability of: a) continuous-time positive systems whose vector fields are homogeneous and cooperative and b) discrete-time positive systems whose vector fields are homogeneous and order-preserving. We then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization. Finally, we extend the results to general linear systems with time-varying delays.

AlkuperäiskieliEnglanti
Artikkeli6675044
Sivut1594-1599
Sivumäärä6
JulkaisuIEEE Transactions on Automatic Control
Vuosikerta59
Numero6
DOI - pysyväislinkit
TilaJulkaistu - 2014
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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