This technical communique extends the recent results of Geromel and Gabriel (2015) to H-infinity, sampled data control design of Markov jump linear systems (MJLS). It fulfills a lack of a specific necessary and sufficient result in the literature of sampled-data control of MJLS in the context of H-infinity performance. Mean square stabilizability and performance determination are addressed and discussed in a unified theoretical viewpoint. As a natural consequence, it is shown that the previous result of Geromel and Gabriel (2015) is obtained as a particular case. A globally uniformly convergent algorithm is proposed to solve the design conditions. The theory is illustrated by means of an example. (C) 2017 Elsevier Ltd. All rights reserved.