On Pade Approximations and the Preservation of Quadratic Stability for Switched Linear Systems
Shorten, R. and Corless, M. and Sajja, S. and Solmaz, S. (2010) On Pade Approximations and the Preservation of Quadratic Stability for Switched Linear Systems. International Journal of Control . ISSN 0020-7179
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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