The idea of the multi-controller approach is to design local controllers, each of them combined with a special environment. One problem of this approach is to select the best local controller or even several controllers in order to design the final control law, which will be applied to the plant. In this paper, a 'switching' algorithm based on a symbolic fuzzy system is used. The main goal is basically to blend the control signals provided by several controllers, which are model-reference output feedback controllers (RST controllers) in our method. Nonetheless, an interesting issue is the stability of the global structure with a reference signal. In this paper, we present research studies on the stability analysis of the proposed multi-controller approach by using Lyapunov theory and linear matrix inequalities (LMIs). The derivative of a candidate quadratic Lyapunov function is calculated thanks to a weighted sum of local derivatives. Finally, a real-time experimentation on a robot wrist shows the effectiveness of the approach.