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Vietnam Journal of Mathematics 35:4(2007)
429-462
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Robust Stability and Transient Behaviour of
Positive Linear Systems
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D. Hinrichsen and
E. Plischke
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Abstract. After a brief review of available
results the main focus of the paper is on the transient behaviour of
positive systems and their stability radii with respect to highly
structured perturbations. Simple upper bounds for the transient gain of
positive systems are obtained by means of linear Lyapunov functions on the
positive orthant. The minimization of these bounds is discussed and
algorithms for computing optimal Lyapunov vectors are presented. By means
of linear Lyapunov functions we get new formulae for the stability radii of
positive linear systems with respect to structured and time-varying
perturbations of Gershgorin-Brualdi type. With every time-invariant linear
system we associate a corresponding positive system and this correspondence
allows to transfer some of the results to non-positive linear systems.
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2000 Mathematics Subject Classification: 37C65, 47A55,
34D20.
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Keywords: Positive systems, transient behaviour,
stability radii, Lyapunov norms, structured uncertainties, time-varying
perturbations.
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Established by
Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published by Springer
since January 2013
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