This paper is concerned with the treatment of saturation nonlinearity existing commonly in practical control systems. An improved treatment of such nonlinearity is proposed, which includes the well-known linear differential inclusion method for handling saturation nonlinearity as a special case. To show the effectiveness of this new treatment, the problem of analysis and design of linear systems subject to nested saturation function is revisited. The proposed results not only complement the existing work on this problem, but also are less conservative than the existing methods. Four numerical examples are worked out to illustrate the applicability of the established approaches. (C) 2010 Elsevier Ltd. All rights reserved.