Abstract In this paper a family of stabilizing boundary feedback control laws for a class of linear parabolic PDEs motivated by engineering applications is presented. The design procedure presented here can handle systems with an arbitrary finite number of open-loop unstable eigenvalues and is not restricted to a particular type of boundary actuation. The stabilization is achieved through the design of coordinate transformations that have the form of recursive relationships. The fundamental difficulty of such transformations is that the recursion has an infinite number of iterations. The problem of feedback gains growing unbounded as grid becomes infinitely fine is resolved by a proper choice of the target system to which the original system is transformed. We show how to design coordinate transformations such that they are sufficiently regular (not continuous but L_∞). We then establish closed—loop stability, regularity of control, and regularity of solutions of the PDE. The result is accompanied by a simulation study for a linearization of a tubular chemical reactor around an unstable steady state.