Explicit Model Predictive Control often has a complex solution in terms of the number of regions required to define the solution and the corresponding memory requirement to represent the solution in the online implementation. An alternative approach to constrained control is based on the use of controlled contractive sets. However, polytopic controlled contractive sets may themselves be relatively complex, leading to a complex explicit solution, and the polytopic structure can limit the size of the controlled contractive set. This paper develops a method to obtain a larger controlled contractive set by allowing higher order functions in the definition of the contractive set, and explores the use of such higher-order contractive sets in controller design leading to a low complexity explicit control formulation. (C) 2018 Elsevier Ltd. All rights reserved.