In this work, a non-uniform multi-rate controller which includes an RST control stage is introduced. Due to several issues, in some systems the use of non-uniform (irregular) multi-rate sampling becomes inevitable. When using a uniform (regular) multi-rate controller in this kind of situations, control performance is usually degraded (if it is compared to that obtained in the nominal, uniform sampling context). Thus, the design of a non-uniform controller proper for this sampling scheme is needed to keep the performance. A sequence of different non-uniform sampling frames can be considered, and different controllers must be designed for each frame using appropriate methods. When switching among these controllers, stability problems can appear. So, the control system stability will be assured in terms of Linear Matrix Inequalities (LMIs). To achieve some advantages at the design step, the discrete-time input output representation will be used. But, since the classical, uniform z(-i) delay operator could not be able to represent non-uniform sampling situations, the so-called non-uniform operator will be required. Simulation results illustrate that this control proposal is able to keep control system performance and preserve stability. (C) 2012 Elsevier Ltd. All rights reserved.