Zappavigna, A. and Colaneri, P. and Kirkland, S. and Shorten, R.
Essentially Negative News About Positive Systems.
In this paper the discretisation 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 discretising continuous time systems and
for control system design. We observe that this method of approximation is not suited
for the discretisation 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
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