In this paper the regulation problem for linear continuous-time systems by linearstate-feedback under linear state and/or control constraints is investigated. This problem, namedthe Linear Constrained Regulation Problem, has been extensively studied when the regulationconcerns an equilibrium situated in the interior of the domain of admissible states. In this paperthe case when the desired equilibrium state is on the boundary of the domain of admissiblestates is considered. The tools used for the analysis and design of this kind of control problemsare the conditions of positive invariance of polyhedral sets, Lyapunov-like polyhedral functions,LMI methods and eigenstructure assignment techniques.