Zappavigna, Annalisa and Colaneri, Patrizio and Kirkland, Steve and Shorten, Robert
On the preservation of co-positive Lyapunov functions under Padé
discretization for positive systems.
In: 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), 5-9 July 2010, Budapest, Hungary.
In this paper the discretization of switched and
non-switched linear positive systems using Padé approximations
is considered. We show:
1) first order diagonal Padé approximation preserves both
linear and quadratic co-positive Lyapunov functions,
higher order transformations need an additional condition
on the sampling time1;
2) positivity need not be preserved even for arbitrarily small
sampling time for certain Padé approximations.
Sufficient conditions on the Padé approximations are given to
preserve positivity of the discrete-time system. Finally, some
examples are given to illustrate the efficacy of our results.
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