A gain scheduling based on a one-parameter family of Lyapunov func-tions is presented for the control of linear systems with aane con-straints. The tuning of the parameter in the control law is assumed to result from a trade-oo between the size of the state-space domain where the constraints are satissed and the closed-loop performance. A target controller is chosen for local performance in this family. The proposed online scheduling is aimed at reaching the target controller in the fastest possible way, while guaranteeing satisfaction of the con-straints along closed-loop solutions.