The problem of constrained regulation of linear systems around an equilibrium situated in the interior of a domain of attraction has been extensively investigated. In many engineering problems however, like obstacle avoidance problems, the regulation around an equilibrium situated on the boundary of the domain of attraction is necessary. For this kind of problems, the classical methods cannot be applied and design control methods are missing. Using invariant set techniques, the present paper proposes design methods for guaranteeing convergence to an equilibrium situated on the boundary of the feasible region, all by respecting the state constraints. A collision avoidance numerical example is presented for illustrating the theoretical results of the paper.