On the preservation of co-positive Lyapunov functions under Padé discretization for positive systems
Zappavigna, Annalisa and Colaneri, Patrizio and Kirkland, Steve and Shorten, Robert (2010) 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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