A scaling and squaring method for the discretisation of positive switched systems

摘要

In this paper we present a new method for approximating the matrix exponential of a Metzler matrix. This method is useful in discretising switched positive systems. In particular, the method preserves both linear and quadratic stability of the original continuous time system, as well as positivity of states starting for initial conditions in the positive orthant. The usefulness of the method is highlighted by illustrating some of the drawbacks of Padé approximations when applied to positive linear systems.