Initial Condition Independent Stabilisability of Switched Affine Systems

We have previously demonstrated that a switched affine system is stabilisable independently of the initial condition, i.e. there exists an asymptotically stabilising switching function which is the same for all initial conditions, if and only if there exists a stable convex combination of the sub-system matrices. This result was proven by constructing a stabilising switching function of unbounded switching frequency. The current paper proves that there exists a switching function with bounded switching frequency which stabilises a switched affine system independent of its initial condition.