A set-membership (SM) approach is proposed to design reliable static stabilizing controllers for non-linear dynamical systems. First, the control design problem is reformulated as a parameter identification issue in an unknown-but-bounded error framework. Then, a new dual set integration method for reachability computation is introduced. Finally, the latter dual method is used in conjunction with set inversion techniques via interval analysis, in order to develop an SM parameter estimation algorithm to solve the control design problem. The identified feedback control must achieve two aims. The first aim is that, starting from a given bounded set of initial states, the state trajectories generated by the controlled non-linear system have to reach in a finite-time a desired target set. The second aim is to ensure asymptotic stability of the controlled system over the target set. The effectiveness of the proposed method is illustrated through a complex non-linear system.