In this paper, the stability analysis and H-infinity control problems for a class of continuous-time switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L-2-gain performance analysis and H-infinity control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results. (C) 2018 Elsevier Ltd. All rights reserved.