Abstract

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.