id: 06034467
dt: j
an: 06034467
au: Zappavigna, A.; Colaneri, P.; Kirkland, S.; Shorten, R.
ti: Essentially negative news about positive systems.
so: Linear Algebra Appl. 436, No. 9, 3425-3442 (2012).
py: 2012
pu: Elsevier Science Inc. (North-Holland), New York, NY
la: EN
cc: 
ut: switching positive systems; discretization; Padé approximation
ci: 
li: doi:10.1016/j.laa.2011.12.021
ab: Summary: In this paper, the discretization of switched and non-switched
    linear positive systems using Padé approximations is considered. Padé
    approximations to the matrix exponential are sometimes used by control
    engineers for discretizing continuous time systems and for control
    system design. We observe that this method of approximation is not
    suited for the discretization of positive dynamic systems, for two key
    reasons. First, certain types of Lyapunov stability are not, in
    general, preserved. Secondly, and more seriously, positivity need not
    be preserved, even when stability is. Finally we present an alternative
    approximation to the matrix exponential which preserves positivity, and
    linear and quadratic stability.
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