Based on the determination of a minimum dwell time, this article addresses the problem of characterising a switching strategy for H-infinity stabilisation of switched linear stochastic systems with adapted external inputs. Sufficient conditions that assure exponential mean square stability and an H-infinity performance index are established by analysing the time evolution of the second-order moment of the state and a recursive dynamic programming inequality, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.