Shorten, R. and Corless, M. and Sajja, S. and Solmaz, S.
On Pade Approximations and the Preservation of
Quadratic Stability for Switched Linear Systems.
International Journal of Control.
In this note we consider the stability preserving properties of diagonal Pad´e approximations
to the matrix exponential. We show that while diagonal Pad´e approximations preserve
quadratic stability when going from continuous-time to discrete-time, the converse is not
true. We discuss the implications of this result for discretising switched linear systems. We
also show that for continuous-time switched systems which are exponentially stable, but not
quadratically stable, a Pad´e approximation may not preserve stability.
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