This brief paper addresses the implementation and well-posedness aspects of multivariable algebraic loops which arise naturally in many anti-windup control schemes. Using the machinery of linear complementarity problems, a unified framework is developed for establishing well-posedness of such algebraic loops. Enforcing well-posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti-windup design stage. Several existing anti-windup implementations appear as special cases of the unified framework presented in this brief paper.