So far, a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean-square stability. This paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean-square sense. The results are expressed in terms of linear matrix inequalities (LMIs) which are easy to be checked in practice by using MATLAB Toolbox. Moreover, the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system. (C) 2007 Elsevier Ltd. All rights reserved.